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7 papers · 1 filter
The Extension for Mean Curvature Flow with Finite Integral Curvature in Riemannian Manifolds
Hong-Wei Xu, Fei Ye, En-Tao Zhao
We investigate the integral conditions to extend the mean curvature flow in a Riemannian manifold. We prove that the mean curvature flow solution with finite total mean curvature o…
Positive mass theorems for asymptotically de Sitter spacetimes
Mingxing Luo, Naqing Xie, Xiao Zhang
We use planar coordinates as well as hyperbolic coordinates to separate the de Sitter spacetime into two parts. These two ways of cutting the de Sitter give rise to two different s…
The hyperbolic geometric flow on Riemann surfaces
De-Xing Kong, Kefeng Liu, De-Liang Xu
In this paper the authors study the hyperbolic geometric flow on Riemann surfaces. This new nonlinear geometric evolution equation was recently introduced by the first two authors…
Complete real Kahler submanifolds in codimension two
Luis A. Florit, Fangyang Zheng
Minimal isometric immersions F in codimension two from a complete Kahler manifold into Euclidean space had been classified for dimension greater than or equal to 3. In this note we…
Hyperbolic geometric flow (I): short-time existence and nonlinear stability
Wen-Rong Dai, De-Xing Kong, Kefeng Liu
In this paper we establish the short-time existence and uniqueness theorem for hyperbolic geometric flow, and prove the nonlinear stability of hyperbolic geometric flow defined on…
Differential Forms and the Noncommutative Residue for Manifolds with Boundary in the Non-product Case
Yong Wang
In this paper, for an even dimensional compact manifold with boundary which has the non-product metric near the boundary, we use the noncommutative residue to define a conformal in…