| Abstract: |
| In this talk, we are concerned on the convexity estimates for solutions of some elliptic problems obtained in the pass few years. By the classical maximum principle, we give the convexity estimates for the solution to the torsion problem, for the first eigenfunction and the Green`s function of the Laplace operator in a convex bounded domain. In addition, we also give some results about the curvature estimates for the level sets of solutions to Monge-Amp\`{e}re equation in
\mathbb{R}^n or space form. |
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