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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
Abstract 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.