论文标题
Poincaré类型的不平等问题和僵化结果
Poincaré type inequality for hypersurfaces and rigidity results
论文作者
论文摘要
在本文中，在对截面曲率的轻度限制下，我们利用了对称内态性的差异公式来推断一般的庞加莱类型不平等。我们将这种不平等应用于空间形式和爱因斯坦歧管的高层曲面的高阶平均曲率，以获得几种等级不平等，以及刚性的结果，可满足完整的R-Minimal Hypersurface，以满足无穷大的第二个基本形式的合适衰减。此外，使用这些技术，我们证明了对一类完全非线性曲率流的自相似解决方案的平坦性和不存在结果。
In this article, under mild constraints on the sectional curvature, we exploit a divergence formula for symmetric endomorphisms to deduce a general Poincaré type inequality. We apply such inequality to higher-order mean curvature of hypersurfaces of space forms and Einstein manifolds, to obtain several isoperimetric inequalities, as well as rigidity results for complete r-minimal hypersurfaces satisfying a suitable decay of the second fundamental form at infinity. Furthermore, using these techniques, we prove flatness and non-existence results for self-similar solutions to a large class of fully nonlinear curvature flows.
