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Right Engel elements of stability groups of general series in vector spaces
http://ddd.uab.cat/record/168353
Let V be an arbitrary vector space over some division ring D, L a general series of subspaces of V covering all of V \ {0} and S the full stability subgroup of L in GL(V). We prove that always the set of bounded right Engel elements of S is equal to the w-th term of the upper central series of S and that the set of right Engel elements of S is frequently equal to the hypercentre of S. Wehrfritz, B. A. F.Mon, 19 Dec 2016 05:29:45 GMThttp://ddd.uab.cat/record/1683532017Localization genus
http://ddd.uab.cat/record/168352
Which spaces look like an n-sphere through the eyes of the n-th Postnikov section functor and the n-connected cover functor? The answer is what we call the Postnikov genus of the n-sphere. We dene in fact the notion of localization genus for any homotopical localization functor in the sense of Bouseld and Dror Farjoun. This includes exotic genus notions related for example to Neisendorfer localization, or the classical Mislin genus, which corresponds to rationalization. Møller, Jesper M.Mon, 19 Dec 2016 05:29:45 GMThttp://ddd.uab.cat/record/1683522017Continuity of solutions to space-varying pointwise linear elliptic equations
http://ddd.uab.cat/record/168351
We consider pointwise linear elliptic equations of the form Lα uα = ŋα on a smooth compact manifold where the operators Lα are in divergence form with real, bounded, measurable coefficients that vary in the space variableα. We establish L2-continuity of the solutions at α whenever the coefficients of Lα are L∞ -continuous at α and the initial datum is L2 -continuous at α. This is obtained by reducing the continuity of solutions to a homogeneous Kato square root problem. As an application, we consider a time evolving family of metrics gt that is tangential to the Ricci flow almost-everywhere along geodesics when starting with a smooth initial metric. Under the assumption that our initial metric is a rough metric on ʍ with a C1 heat kernel on a “non-singular" nonempty open subset Ɲ, we show that α à gt (α) is continuous whenever α € Ɲ. Bandara, LashiMon, 19 Dec 2016 05:29:45 GMThttp://ddd.uab.cat/record/1683512017Blow-up solutions for some nonlinear elliptic equations involving a Finsler-Laplacian
http://ddd.uab.cat/record/168350
Della Pietra, FrancescoMon, 19 Dec 2016 05:29:45 GMThttp://ddd.uab.cat/record/1683502017Equigeneric and equisingular families of curves on surfaces
http://ddd.uab.cat/record/168349
We investigate the following question: let C be an integral curve contained in a smooth complex algebraic surface X; is it possible to deform C in X into a nodal curve while preserving its geometric genus? We armatively answer it in most cases when X is a Del Pezzo or Hirzebruch surface (this is due to Arbarello and Cornalba, Zariski, and Harris), and in some cases when X is a K3 surface. Partial results are given for all surfaces with numerically trivial canonical class. We also give various examples for which the answer is negative. Dedieu, ThomasMon, 19 Dec 2016 05:29:45 GMThttp://ddd.uab.cat/record/1683492017An example pertaining to the failure of the Besicovitch-Federer structure theorem in Hilbert space
http://ddd.uab.cat/record/168348
We give an example, in the innite dimensional separable Hilbert space, of a purely unrectiable Borel set with nite nonzero one dimensional Hausdor measure, whose projection is nonnegligible in a set of directions which is not Aronszajn null. De Pauw, ThierryMon, 19 Dec 2016 05:29:45 GMThttp://ddd.uab.cat/record/1683482017Low energy canonical immersions into hyperbolic manifolds and standard spheres
http://ddd.uab.cat/record/168347
We consider critical points of the global L2-norm of the second fundamental form, and of the mean curvature vector of isometric immersions of compact Riemannian manifolds into a fixed background Riemannian manifold, as functionals over the space of deformations of the immersion. We prove new gap theorems for these functionals into hyperbolic manifolds, and show that the celebrated gap theorem for minimal immersions into the standard sphere can be cast as a theorem about their critical points having constant mean curvature function, and whose second fundamental form is suitably small in relation to it. In this case, the various minimal submanifolds that occur at the pointwise upper bound on the norm of the second fundamental form are realized by manifolds of nonnegative Ricci curvature, and of these, the Einstein ones are distinguished from the others by being those that are immersed on the sphere as critical points of the first of the functionals mentioned. del Rio, HebertoMon, 19 Dec 2016 05:29:45 GMThttp://ddd.uab.cat/record/1683472017A formula for the Dubrovnik polynomial of rational knots
http://ddd.uab.cat/record/168346
We provide a formula for the Dubrovnik polynomial of a rational knot in terms of the entries of the tuple associated with a braid-form diagram of the knot. Our calculations can be easily carried out using a computer algebra system. Caprau, CarmenMon, 19 Dec 2016 05:29:44 GMThttp://ddd.uab.cat/record/1683462017A Marcinkiewicz integral type characterization of the Sobolev space
http://ddd.uab.cat/record/168345
In this paper we present a new characterization of the Sobolev space W1,p , 1 < p < ∞ which is a higher dimensional version of a result of Waterman [32]. We also provide a new and simplified proof of a recent result of Alabern, Mateu, and Verdera [2]. Finally, we generalize the results to the case of weighted Sobolev spaces with respect to a Muckenhoupt weight. Hajlasz, PiotrMon, 19 Dec 2016 05:29:44 GMThttp://ddd.uab.cat/record/1683452017Automorphisms groups of simplicial complexes of infinite type surfaces
http://ddd.uab.cat/record/168344
Let S be an orientable surface of innite genus with a nite numberof boundary components. In this work we consider the curve complex C(S), the nonseparating curve complex N(S), and the Schmutz graph G(S) of S. When all topological ends of S carry genus, we show that all elements in the automorphismgroups Aut(C(S)), Aut(N(S)), and Aut(G(S)) are geometric, i. e. these groups are naturally isomorphic to the extended mapping class group MCG(S) of the innite surface S. Finally, we study rigidity phenomena within Aut(C(S)) and Aut(N(S)). Hernández Hernández, JesúsMon, 19 Dec 2016 05:29:44 GMThttp://ddd.uab.cat/record/1683442017Bilinear weighted Hardy inequality for nonincreasing functions
http://ddd.uab.cat/record/168343
Krepela, MartinMon, 19 Dec 2016 05:29:44 GMThttp://ddd.uab.cat/record/1683432017Common zeros preserving maps on vector-valued function spaces and Banach modules
http://ddd.uab.cat/record/160583
Let X, Y be Hausdorff topological spaces, and let E and F be Hausdorff topological vector spaces. For certain subspaces A (X,E) and A(Y, F) of C(X,E) and C(Y, F) respectively (including the spaces of Lipschitz functions), we characterize surjections S, T : A (X;E) → A(Y, F), not assumed to be linear, which jointly preserve common zeros in the sense that Z (f – f’) ∩ Z (f – f’) ∩ Z (g – g’) ≠ 0 if and only if Z (Sf – Sf’) ∩ Z (Tg – Tg´) ≠ 0 for all f, f’, g, g’ ∈ A (X, E). Here Z (·)denotes the zero set of a function. Using the notion of point multipliers we extend the notion of zero set for the elements of a Banach module and give a representation for surjective linear maps which jointly preserve common zeros in module case. Hosseini, MalihehThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605832016Convergence of functions of self-adjoint operators and applications
http://ddd.uab.cat/record/160582
The main result (roughly) is that if Hi converges weakly to H and if also f (Hi) converges weakly to f(H), for a single strictly convex continuous function f, then (Hi) must converge strongly to H. One application is that if f(pr(H)) = pr(f(H)), where pr denotes compression to a closed subspace M, then M must be invariant for H. A consequence of this is the verification of a conjecture of Arveson, that Theorem 9. 4 of [Arv] remains true in the infinite dimensional case. And there are two applications to operator algebras. If h and f(h) are both quasimultipliers, then h must be a multiplier. Also (still roughly stated), if h and f(h) are both in pAsap, for a closed projection p, then h must be strongly q-continuous on p. Brown, Lawrence G.Thu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605822016Global well-posedness and symmetries for dissipative active scalar equations with positive-order couplings
http://ddd.uab.cat/record/160581
We consider a family of dissipative active scalar equations outside the L2-space. This was introduced in [7] and its velocity fields are coupled with the active scalar via a class of multiplier operators which morally behave as derivatives of positive order. We prove global well-posedness and time-decay of solutions, with-out smallness assumptions, for initial data belonging to the critical Lebesgue space Ln/2y-β (ℝn ) which is a class larger than that of the above reference. Symmetry properties of solutions are investigated depending on the symmetry of initial data and coupling operators. Ferreira, Lucas C. F.Thu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605812016Röver's simple group is of type F ∞
http://ddd.uab.cat/record/160580
We prove that Claas Röver's Thompson-Grigorchuk simple group V G has type F∞. The proof involves constructing two complexes on which V G acts: a simplicial complex analogous to the Stein complex for V , and a polysimplicial complex analogous to the Farley complex for V . We then analyze the descending links of the polysimplicial complex, using a theorem of Belk and Forrest to prove increasing connectivity. Belk, JamesThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605802016Integral restriction for bilinear operators
http://ddd.uab.cat/record/160579
We consider the integral domain restriction operator TΩ for certain bilinear operator T. We obtain that if (s, p1, p2) satisfies 1 p1+ 1 p2 ≥ 2 min{1,s} and kTkLp1 ×Lp2→Ls < ∞, then kTΩkLp1 ×Lp2→Ls < ∞. For some special domain Ω, this property holds for triplets (s, p1, p2) satisfying 1 p1 + 1 p2 > 1 min{1,s}. Zhao, WeirenThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605792016The Kato Square Root Problem follows from an extrapolation property of the Laplacian
http://ddd.uab.cat/record/160578
On a domain Ω ⊆ _ Rd we consider second-order elliptic systems in divergence-form with bounded complex coefficients, realized via a sesquilinear form with domain H1/0 (Ω) ⊆ V ⊆ H1 (Ω). Under very mild assumptions on Ω and V we show that the solution to the Kato Square Root Problem for such systems can be deduced from a regularity result for the fractional powers of the negative Laplacian in the same geometric setting. This extends earlier results of McIntosh [25] and Axelsson-Keith-McIntosh [6] to non-smooth coefficients and domains. Egert, MoritzThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605782016A monotonicity formula for minimal sets with a sliding boundary condition
http://ddd.uab.cat/record/160577
We prove a monotonicity formula for minimal or almost minimal sets for the Hausdorff measure Hd, subject to a sliding boundary constraint where competitors for E are obtained by deforming E by a one-parameter family of functions yt such that yt(x) ∈ L when x ∈ E lies on the boundary L. In the simple case when L is an affine subspace of dimension d-1, the monotone or almost monotone functional is given by F(r) = r-d Hd (E∩B(x, r)) + r-d Hd (S∩B(x,r)) where x is any point of E (not necessarily on L) and S is the shade of L with a light at x. We then use this, the description of the case when F is constant, and a limiting argument, to give a rough description of E near L in two simple cases. David, GuyThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605772016Vitali's theorem without uniform boundedness
http://ddd.uab.cat/record/160576
Let {fm}m≥1 be a sequence of holomorphic functions defined on a bounded domain D ⊂ Cn or a sequence of rational functions (1 ≤ deg rm ≤ m) defined on Cn. We are interested infinding sufficient conditions to ensure the convergence of {fm}m≥1 on a large set provided the convergence holds pointwise on a not too small set. This type of result is inspired from a theorem of Vitali which gives a positive answer for uniformly bounded sequence. Quang Dieu, NguyenThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605762016Summation of coefficients of polynomials on Lp spaces
http://ddd.uab.cat/record/160575
We investigate the summability of the coefficients of m-homogeneous polynomials and m-linear mappings defined on `p spaces. In our research we obtain results on the summability of the coefficients of m-linear mappings defined on Lp1 x . . . x Lpm. The first results in this respect go back to Littlewood [17] and Bohnenblust and Hille [6] for bilinear and m-linear forms on c0, and Hardy and Littlewood [15] and Praciano-Pereira [20] for bilinear and m-linear forms on arbitrary `p spaces. Our results recover and in some case complete these old results through a general approach on vector valued m-linear mappings. Dimant, VerónicaThu, 14 Jul 2016 06:36:06 GMThttp://ddd.uab.cat/record/1605752016Entire spacelike -graphs in Lorentzian product spaces
http://ddd.uab.cat/record/160574
In this work we establish suffcient conditions to ensure that an entire spacelike graph immersed with constant mean curvature in a Lorentzian product space, whose Riemannian fiber has sectional curvature bounded from below, must be a trivial slice of the ambient space. Lima, Henrique F. deThu, 14 Jul 2016 06:36:05 GMThttp://ddd.uab.cat/record/1605742016On the global asymptotic stability of difference equations satisfying a Markus-Yamabe condition
http://ddd.uab.cat/record/150744
We prove a global asymptotic stability result for maps coming from n-th order difference equation and satisfying a Markus-Yamabe type condition. We also show that this result is sharp. Cima, AnnaFri, 06 May 2016 08:59:52 GMThttp://ddd.uab.cat/record/1507442014Non-algebraic oscillations for predator-prey models
http://ddd.uab.cat/record/150737
We prove that the limit cycle oscillations of the celebrated Rosenzweig-MacArthur differential system and other predator-prey models are non-algebraic. Ferragut, AntoniFri, 06 May 2016 08:59:52 GMThttp://ddd.uab.cat/record/1507372014Random interval homeomorphisms
http://ddd.uab.cat/record/150736
We investigate homeomorphisms of a compact interval, applied randomly. We consider this system as a skew product with the two-sided Bernoulli shift in the base. If on the open interval there is a metric in which almost all maps are contractions, then (with mild additional assumptions) there exists a global pullback attractor, which is a graph of a function from the base to the fiber. It is also a forward attractor. However, the value of this function depends only on the past, so when we take the one-sided shift in the base, it disappears. We illustrate those phenomena on an example, where there are two piecewise linear homeomorphisms, one moving points to the right and the other one to the left. Alsedà, LluísFri, 06 May 2016 08:59:52 GMThttp://ddd.uab.cat/record/1507362014Polynomial and rational first integrals for planar homogeneous polynomial differential systems
http://ddd.uab.cat/record/150716
In this paper we find necessary and sufficient conditions in order that a planar homogeneous polynomial differential system has a polynomial or rational first integral. We apply these conditions to linear and quadratic homogeneous polynomial differential systems. Giné, JaumeFri, 06 May 2016 08:59:51 GMThttp://ddd.uab.cat/record/1507162014