论文标题
卡坦 - 哈达马德歧管中的冷水微米熵
Colding-Minicozzi Entropies in Cartan-Hadamard Manifolds
论文作者
论文摘要
我们在cartan-hadamard歧管的子手机上介绍了一系列功能，这些功能概括了欧几里得空间的submanifolds的冷水微Zi熵。我们表明，在自然条件下，这些功能在平均曲率流下是单调的。结果，我们在某些封闭的超曲面上获得了这些熵的尖锐下限，并观察到一种新颖的刚性现象。
We introduce a family of functionals on submanifolds of Cartan-Hadamard manifolds that generalize the Colding-Minicozzi entropy of submanifolds of Euclidean space. We show that these functionals are monotone under mean curvature flow under natural conditions. As a consequence, we obtain sharp lower bounds on these entropies for certain closed hypersurfaces and observe a novel rigidity phenomenon.
