Local monotonicity of measures supported by graphs of convex functions
Cerny, Robert (Charles University (Praga, República Txeca). Department of Mathematical Analysis)

Date:	2004
Abstract:	Let f ∈ C2 (R) satisfy f(0) = f 0 (0) = 0 and f 00(0) > 0. Then the 1-dimensional Hausdorff measure restricted to the graph of f is locally monotone near the origin in the sense that there exists σ > 0 such that the function r 7→ µf B(z,r) r is nondecreasing on (0, σ) for every centre z ∈ B(σ). The result is reformulated for Hausdorff measures restricted to uniformly C2 -curves in R 2 with the curvature bounded away from zero and infinity.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Monotone measure ; Monotonicity formula
Published in:	Publicacions matemàtiques, V. 48 N. 2 (2004) , p. 369-380, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/38101
DOI: 10.5565/PUBLMAT_48204_04

12 p, 151.5 KB

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