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Gaussian curvature estimates for the convex level sets of p ‐harmonic functions
Author(s) -
Ma XiNan,
Ou Qianzhong,
Zhang Wei
Publication year - 2010
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.20318
Subject(s) - mathematics , gaussian curvature , harmonic function , convexity , curvature , mathematical analysis , regular polygon , boundary (topology) , norm (philosophy) , pseudoconvex function , harmonic , gaussian , pure mathematics , geometry , convex combination , convex optimization , physics , quantum mechanics , political science , financial economics , law , economics
We give a positive lower bound for the Gaussian curvature of the convex level sets of p ‐harmonic functions with the Gaussian curvature of the boundary and the norm of the gradient on the boundary. Combining the deformation process, this estimate gives a new approach to studying the convexity of the level sets of the p ‐harmonic function. © 2010 Wiley Periodicals, Inc.