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Curvature Estimates for the Level Sets of Solutions to the Monge-Amp`ere Equation detD2u = 1 |
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| Authors: | Chuanqiang CHEN Xinan MA and Shujun SHI |
| Institution: | 1. Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Hefei 230026, China 2. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China 3. School of Mathematical Sciences, Harbin Normal University, Harbin 150025,China |
| Abstract: | For the Monge-Ampère equation detD 2 u = 1, the authors find new auxiliary curvature functions which attain their respective maxima on the boundary. Moreover, the upper bounded estimates for the Gauss curvature and the mean curvature of the level sets for the solution to this equation are obtained. |
| Keywords: | Curvature estimates Level sets Monge-Ampère equation |
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