In this paper,the authors can prove the existence of translating solutions to the nonparametric mean curvature flow with nonzero Neumann boundary data in a prescribed product manifold M^(n)×R,where M^(n) is an n-...In this paper,the authors can prove the existence of translating solutions to the nonparametric mean curvature flow with nonzero Neumann boundary data in a prescribed product manifold M^(n)×R,where M^(n) is an n-dimensional(n≥2)complete Riemannian manifold with nonnegative Ricci curvature,and R is the Euclidean 1-space.展开更多
In this paper,we consider the Neumann problem for parabolic Hessian quotient equations.We show that the k-admissible solution of the parabolic Hessian quotient equation exists for all time and converges to the smooth ...In this paper,we consider the Neumann problem for parabolic Hessian quotient equations.We show that the k-admissible solution of the parabolic Hessian quotient equation exists for all time and converges to the smooth solution of elliptic Hessian quotient equations.Also solutions of the classical Neumann problem converge to a translating solution.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11801496,11926352)the Fok Ying-Tung Education Foundation(China)Hubei Key Laboratory of Applied Mathematics(Hubei University)。
文摘In this paper,the authors can prove the existence of translating solutions to the nonparametric mean curvature flow with nonzero Neumann boundary data in a prescribed product manifold M^(n)×R,where M^(n) is an n-dimensional(n≥2)complete Riemannian manifold with nonnegative Ricci curvature,and R is the Euclidean 1-space.
基金Supported by NSFC(Grant Nos.11771396,11721101,11871255 and 11901102)China Postdoctoral Science Foundation(Grant No.2019M651333)。
文摘In this paper,we consider the Neumann problem for parabolic Hessian quotient equations.We show that the k-admissible solution of the parabolic Hessian quotient equation exists for all time and converges to the smooth solution of elliptic Hessian quotient equations.Also solutions of the classical Neumann problem converge to a translating solution.
