Gaussian curvature estimates for the convex level sets of p‐harmonic functions |
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| Authors: | Xi‐Nan Ma Qianzhong Ou Wei Zhang |
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| Institution: | 1. University of Science and Technology of China, Department of Mathematics, Hefei 230026 Anhui Province, P.R. China;2. Hezhou University, Department of Mathematics, Hezhou 542800 Guangxi Province, P.R. China |
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| Abstract: | 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. |
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