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Primary 31B15, 28A75; Secondary 35R35 Keywords: Author: Xavier Tolsa; Tatiana Toro Creator: LaTeX with hyperref package Producer: Acrobat Distiller Server 8.1.0 (Pentium Linux, Built: 2007-09-07) CreationDate: Fri Nov 15 15:51:06 2024 CET ModDate: Fri Nov 15 15:51:06 2024 CET Custom Metadata: yes Metadata Stream: yes Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 22 Encrypted: no Page size: 504 x 720 pts Page rot: 0 File size: 313483 bytes Optimized: yes PDF version: 1.4 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- EOGNMB+CMR10 Type 1C Custom yes yes yes 558 0 EOGNME+CMR7 Type 1C Custom yes yes yes 557 0 EOGNMG+CMMI10 Type 1C Custom yes yes yes 556 0 EOGNMI+CMSY7 Type 1C Custom yes yes yes 555 0 EOGNMJ+CMSY10 Type 1C Custom yes yes yes 554 0 EOGNML+CMMI7 Type 1C Custom yes yes yes 553 0 EOGNMM+CMSY5 Type 1C Custom yes yes yes 575 0 EOGNNA+CMEX10 Type 1C Custom yes yes no 580 0 EOGNNC+CMTI8 Type 1C Custom yes yes yes 579 0 EOGNKL+CMR6 Type 1C Custom yes yes yes 521 0 EOGNKO+CMTT8 Type 1C Custom yes yes yes 522 0 EOGNLA+CMBX10 Type 1C Custom yes yes yes 523 0 EOGNLD+CMR8 Type 1C Custom yes yes yes 524 0 EOGNLF+CMCSC10 Type 1C Custom yes yes yes 525 0 EOGNLG+CMSY8 Type 1C Custom yes yes yes 526 0 EOGNLI+MSBM10 Type 1C Custom yes yes yes 527 0 EOGNLK+CMMI6 Type 1C Custom yes yes yes 528 0 EOGNLM+CMMI8 Type 1C Custom yes yes yes 529 0 EOGNLO+CMSY6 Type 1C Custom yes yes yes 530 0 EOGNMA+CMR5 Type 1C Custom yes yes yes 552 0 EOGNNJ+CMMI5 Type 1C Custom yes yes yes 243 0 EOGNNL+CMTI10 Type 1C Custom yes yes yes 248 0 EOGNNO+MSPM Type 1C Custom yes yes no 254 0 EOGNOO+MSAM10 Type 1C Custom yes yes no 257 0 EOGNPG+esint10 Type 1C Custom yes yes yes 262 0 EOGOAJ+MSBM7 Type 1C Custom yes yes yes 264 0 EOGODG+CMSS10 Type 1C Custom yes yes yes 265 0 EOGODH+CMSS8 Type 1C Custom yes yes yes 268 0 EOGOGH+CMEX7 Type 1C Custom yes yes no 271 0 EOGOHC+CMBX8 Type 1C Custom yes yes yes 276 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2026-02-10 04:13:00 CET RepresentationInformation: traamemat_a2024m11v11p1294-1315.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2026-02-09 17:04:41 CET Size: 313483 Format: PDF Version: 1.4 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf Profile: Linearized PDF PDFMetadata: Objects: 619 FreeObjects: 1 IncrementalUpdates: 1 DocumentCatalog: PageLayout: SinglePage PageMode: UseOutlines Outlines: Item: Title: 1. Introduction Destination: section.1 Item: Title: 2. Preliminaries Destination: section.15 Children: Item: Title: 2.1. Measures and rectifiability Destination: subsection.16 Item: Title: 2.2. Harmonic measure Destination: subsection.19 Item: Title: 2.3. NTA and Reifenberg flat domains Destination: subsection.21 Item: Title: 2.4. The space 𝑉𝑀𝑂 Destination: subsection.28 Item: Title: 2.5. Dyadic lattices and densities Destination: subsection.30 Item: Title: 3. Proof of Theorem 1.1 Destination: section.37 Children: Item: Title: 3.1. Proof of (d) ⇒ (a) Destination: subsection.38 Item: Title: 3.2. Stopping cubes for the proof of (c) ⇒ (d) Destination: subsection.39 Item: Title: 3.3. Proof of Theorem 1.1 using Lemma 3.3 Destination: subsection.48 Item: Title: 4. The proof of Lemma 3.3 Destination: section.54 Children: Item: Title: 4.1. Preliminaries for the construction of the approximating Lipschitz graph Destination: subsection.55 Item: Title: 4.2. The approximating Lipschitz graph Destination: subsection.73 Item: Title: 4.3. The Lipschitz graph Γ and ∂Ω⁺ are close to each other Destination: subsection.86 Item: Title: 4.4. The domains ̃𝑈⁺ and ̃𝑈⁻ Destination: subsection.92 Item: Title: 4.5. Proof of (3.4) Destination: subsection.101 Item: Title: References Destination: section*.111 Info: Title: The two-phase problem for harmonic measure in VMO and the chord-arc condition Author: Xavier Tolsa; Tatiana Toro Subject: 2020 Mathematics Subject Classification. 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