Harnack inequalities on manifolds with boundary and applications
Harnack inequalities on manifolds with boundary and applications
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DOI：
10.1016/j.matpur.2010.03.001
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发表时间：
2009-08
期刊：
影响因子：
--
通讯作者：
Feng-Yu Wang
中科院分区：
文献类型：
--
作者：
Feng-Yu Wang
在一个大类的带边界的黎曼流形上，证明了Neumann半群的一些无量纲Harnack不等式等价于边界的凸性和曲率条件.特别地，对于pt（x，y），Neumann热核w.r.t.一个体积型测度μ，且K为常数，曲率条件Ric− <$Z <$K连同边界的凸性等价于热核熵不等式：其中ρ是黎曼距离。将主要结果部分推广到具有非凸边界的流形，并应用于推导HWI不等式。
On a large class of Riemannian manifolds with boundary, some dimension-free Harnack inequalities for the Neumann semigroup are proved to be equivalent to the convexity of the boundary and a curvature condition. In particular, for pt(x,y) the Neumann heat kernel w.r.t. a volume type measure μ and for K a constant, the curvature condition Ric−∇Z⩾K together with the convexity of the boundary is equivalent to the heat kernel entropy inequality: where ρ is the Riemannian distance. The main result is partly extended to manifolds with non-convex boundary and applied to derive the HWI inequality.