A Frequency Function and Singular Set Bounds for Branched Minimal Immersions | Zendy

Simon Leon | Zendy; Wickramasekera Neshan | Zendy

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A Frequency Function and Singular Set Bounds for Branched Minimal Immersions

Author(s) -

Simon Leon,

Wickramasekera Neshan

Publication year - 2016

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.21642

Subject(s) - mathematics , monotonic function , hausdorff dimension , function (biology) , hausdorff space , dimension (graph theory) , hausdorff distance , set (abstract data type) , class (philosophy) , pure mathematics , mathematical analysis , surface (topology) , combinatorics , discrete mathematics , geometry , evolutionary biology , programming language , biology , artificial intelligence , computer science

We establish a frequency function monotonicity formula for two‐valued C 1,α solutions to the minimal surface system on n ‐dimensional domains. We also establish the sharp regularity result that such solutions are of class C 1, 1/2 , and that their branch sets, if nonempty, have Hausdorff dimension equal to n ‐2.© 2016 Wiley Periodicals, Inc.

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