Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds
Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds
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DOI：
10.1515/crelle-2019-0006
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发表时间：
2017-03
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影响因子：
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通讯作者：
Paul Bryan;Mohammad N. Ivaki;Julian Scheuer
中科院分区：
文献类型：
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作者：
Paul Bryan;Mohammad N. Ivaki;Julian Scheuer
摘要我们得到了具有常非负截面曲率的黎曼流形以及Lorentzian Minkowski和de Sitter空间中一类曲率流的Harnack估计。此外，我们证明了一个Harnack估计与奖金项的平均曲率流的局部对称黎曼爱因斯坦流形的非负截面曲率。利用严格凸超曲面的“对偶”概念，我们还得到了球面和双曲空间中扩张流的一个新的不等式，即所谓的“伪”Harnack不等式.
Abstract We obtain Harnack estimates for a class of curvature flows in Riemannian manifolds of constant nonnegative sectional curvature as well as in the Lorentzian Minkowski and de Sitter spaces. Furthermore, we prove a Harnack estimate with a bonus term for mean curvature flow in locally symmetric Riemannian Einstein manifolds of nonnegative sectional curvature. Using a concept of “duality” for strictly convex hypersurfaces, we also obtain a new type of inequality, so-called “pseudo”-Harnack inequality, for expanding flows in the sphere and in the hyperbolic space.