A sharp strong maximum principle and a sharp unique continuation theorem for singular minimal hypersurfaces

We prove the two theorems of the title, settling two long standing questions in the local theory of singular minimal hypersurfaces. The sharpness of either result is with respect to its hypothesis on the size of the allowable singular sets. The proofs of both theorems rely heavily on the author’s re...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 51; no. 3-4; pp. 799 - 812
Main Author Wickramasekera, Neshan
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2014
Springer Nature B.V
Subjects
Analysis
Calculus
Calculus of variations
Calculus of Variations and Optimal Control; Optimization
Control
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Maximum principle
Partial differential equations
Regularity
Settling
Sharpness
Systems Theory
Theorems
Theoretical
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Summary:We prove the two theorems of the title, settling two long standing questions in the local theory of singular minimal hypersurfaces. The sharpness of either result is with respect to its hypothesis on the size of the allowable singular sets. The proofs of both theorems rely heavily on the author’s recent regularity and compactness theory for stable minimal hypersurfaces, and on earlier work of Ilmanen, Simon and Solomon–White.
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ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-013-0695-4