The authors introduce the Hausdorff convergence to discuss the differentiable sphere theorem with excess pinching. Finally, a type of rigidity phenomenon on Riemannian manifolds is derived.
For the maximal space-like hypersurface defined on 2-dimensional space forms,based on the regularity and the strict convexity of the level sets,the steepest descents are well defined.In this paper,we come to estimate ...For the maximal space-like hypersurface defined on 2-dimensional space forms,based on the regularity and the strict convexity of the level sets,the steepest descents are well defined.In this paper,we come to estimate the curvature of its steepest descents by deriving a differential equality.展开更多
In this paper,we study the mean curvature flow with oblique derivative boundary conditions.We prove the longtime existence by choosing a suitable auxiliary function.Also,we prove the asymptotic behavior of the mean cu...In this paper,we study the mean curvature flow with oblique derivative boundary conditions.We prove the longtime existence by choosing a suitable auxiliary function.Also,we prove the asymptotic behavior of the mean curvature flow with zero oblique derivative boundary data which is a generalization of Huisken’s original result about prescribed perpendicular contact angle.展开更多
基金supported by the National Natural Science Foundation of China (No. 10671066)the Scientific Research Foundation of Qufu Normal University and the Shanghai and Shandong Priority Academic Discipline
文摘The authors introduce the Hausdorff convergence to discuss the differentiable sphere theorem with excess pinching. Finally, a type of rigidity phenomenon on Riemannian manifolds is derived.
基金the National Natural Science Foundation of China(Grant No.11471188)the STPF of Shandong Province(No.J17KA161).
文摘For the maximal space-like hypersurface defined on 2-dimensional space forms,based on the regularity and the strict convexity of the level sets,the steepest descents are well defined.In this paper,we come to estimate the curvature of its steepest descents by deriving a differential equality.
基金supported by National Natural Science Foundation of China(Grant No.11471188)。
文摘In this paper,we study the mean curvature flow with oblique derivative boundary conditions.We prove the longtime existence by choosing a suitable auxiliary function.Also,we prove the asymptotic behavior of the mean curvature flow with zero oblique derivative boundary data which is a generalization of Huisken’s original result about prescribed perpendicular contact angle.
