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本文首先给出了具有渐近非负Ricci曲率流形的体积比较定理. 然后给出了流形在一定的曲率衰减的条件下为有限拓扑型的引理，最后利用Abresch-Gromoll估计, 给出了具有渐近非负Ricci曲率和无穷远处二次曲率衰减的流形的有限拓扑型条件.
CURVATURE PINCHING ESTIMATE AND SINGULARITIES OF THE RICCI FLOW
SINGULARITIES CURVATURE PINCHING ESTIMAT
2015/8/17
In this paper, we first derive a pinching estimate on the traceless Ricci
curvature in term of scalar curvature and Weyl tensor under the Ricci flow. Then
we apply this estimate to study...
THE CONJUGATE HEAT EQUATION AND ANCIENT SOLUTIONS OF THE RICCI FLOW
ANCIENT SOLUTIONS CONJUGATE HEAT EQUATION
2015/8/17
We prove Gaussian type bounds for the fundamental solution of the conjugate heat equation evolving under the Ricci flow. As a consequence, for dimension 4 and
higher, we show that the backward ...
The shifted wave equation on Damek--Ricci spaces and on homogeneous trees
Abel transform Damek–Ricci space homogeneous tree Huygens’ principle hyperbolic space wave equation wave propagation
2012/6/27
We solve explicitly the shifted wave equation on Damek--Ricci spaces, using Asgeirsson's theorem and the inverse dual Abel transform. As an application, we investigate Huygens' principle. A similar an...
Quasilinear Parabolic Equations and the Ricci Flow on Manifolds with Boundary
Quasilinear Parabolic Equations Ricci Manifolds with Boundary
2011/1/21
The first part of the paper discusses a second-order quasilinear parabolic equation in a vector bundle over a compact manifold M with boundary @M. We establish a short-time existence theorem for this ...
Compact Mean Convex Hypersurfaces and the Fundamental Group of Manifolds with Nonnegative Ricci Curvature
Compact Mean Convex Hypersurfaces Fundamental Group of Manifolds Nonnegative Ricci Curvature
2011/1/19
We show that the existence of an embedded compact, boundaryless hypersurface S of strictly
positive mean curvature in a noncompact, connected, complete Riemannian n-manifold N of non-
negative Ricci...
Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow
Differential Harnack inequality Interpolated Harnack inequality Nonlinear
2010/12/1
In this paper, we prove several differential Harnack inequalities for positive solutions of nonlinear (backward) heat equations with different potentials under the Ricci flow. In particular, for a clo...