We investigate a special timelike surfaces in Anti de Sitter 3-space.We call such a timelike surface an Anti de Sitter horospherical flat surface which belongs to a class of surfaces given by one parameter families of...We investigate a special timelike surfaces in Anti de Sitter 3-space.We call such a timelike surface an Anti de Sitter horospherical flat surface which belongs to a class of surfaces given by one parameter families of Anti de Sitter horocycle.We give a generic classification of singularities and study the geometric properties of such surfaces from the viewpoint of Legendrian singularity theory.展开更多
We consider the area-preserving mean curvature flow with free Neumann boundaries. We show that a rotationally symmetric n-dimensional hypersurface in R^(n+1)between two parallel hyperplanes will converge to a cylinder...We consider the area-preserving mean curvature flow with free Neumann boundaries. We show that a rotationally symmetric n-dimensional hypersurface in R^(n+1)between two parallel hyperplanes will converge to a cylinder with the same area under this flow. We use the geometric properties and the maximal principle to obtain gradient and curvature estimates, leading to long-time existence of the flow and convergence to a constant mean curvature surface.展开更多
Abstract In this paper, we explore the fixed point theory of n-vaiued maps using configuration spaces and braid groups, focusing on two fundamental problems, the Wecken property, and the computation of the Nielsen num...Abstract In this paper, we explore the fixed point theory of n-vaiued maps using configuration spaces and braid groups, focusing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the projective plane （resp. the 2-sphere S2） has the Wecken property for n-valued maps for all n ∈N （resp. all n ≥ 3）. In the case n = 2 and S2, we prove a partial result about the Wecken property. We then describe the Nielsen number of a non-split n-valued map φ ： X → X of an orientable, compact manifold without boundary in terms of the Nielsen coincidence numbers of a certain finite covering q： ）→ X with a subset of the coordinate maps of a lift of the n-valued split map → q ： →X.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11101072 and 11271063)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘We investigate a special timelike surfaces in Anti de Sitter 3-space.We call such a timelike surface an Anti de Sitter horospherical flat surface which belongs to a class of surfaces given by one parameter families of Anti de Sitter horocycle.We give a generic classification of singularities and study the geometric properties of such surfaces from the viewpoint of Legendrian singularity theory.
文摘We consider the area-preserving mean curvature flow with free Neumann boundaries. We show that a rotationally symmetric n-dimensional hypersurface in R^(n+1)between two parallel hyperplanes will converge to a cylinder with the same area under this flow. We use the geometric properties and the maximal principle to obtain gradient and curvature estimates, leading to long-time existence of the flow and convergence to a constant mean curvature surface.
基金supported by Fundao de Amparo a Pesquisa do Estado de So Paulo(FAPESP)Projeto Temtico Topologia Algébrica,Geométrica e Diferencial(Grant No.2012/24454-8)supported by the same project as well as the Centre National de la Recherche Scientifique(CNRS)/Fundao de Amparo a Pesquisa do Estado de So Paulo(FAPESP)Projet de Recherche Conjoint(PRC)project(Grant No.275209)
文摘Abstract In this paper, we explore the fixed point theory of n-vaiued maps using configuration spaces and braid groups, focusing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the projective plane （resp. the 2-sphere S2） has the Wecken property for n-valued maps for all n ∈N （resp. all n ≥ 3）. In the case n = 2 and S2, we prove a partial result about the Wecken property. We then describe the Nielsen number of a non-split n-valued map φ ： X → X of an orientable, compact manifold without boundary in terms of the Nielsen coincidence numbers of a certain finite covering q： ）→ X with a subset of the coordinate maps of a lift of the n-valued split map → q ： →X.
