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关于Minkowski投影映射在R^3中浸入的充分条件
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作者 钟建华 《广东教育学院学报》 2004年第2期18-20,共3页
由Minkowski投影映射Φ:M2R3的表达式知Φ是连续且光滑的映射;进一步推证得出当M2是R3中2维紧致凸流形和每一点x处rankxΦ=2时,(Φ,M2)是M2到R3中的2维光滑浸入,而且Φ(M2)是R3中的嵌入紧子流形.
关键词 光滑流形 光滑映射 Minkowski投影映射 光滑浸入 切映射
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LIFE SPAN OF A SMOOTH SOLUTION FOR THE SURFACE DIFFUSION FLOW
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作者 LIU ZUHAN Department of Mathematics, Yangzhou University, Yangzhou 225002, Jiangsu, China. 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2003年第3期331-342,共12页
Consider the motion of immersed hypersurfaces driven by surface diffusion flow and give anlower bound on the life span of a smooth immersed solution, which depends only on how muchthe curvature of the initial surface ... Consider the motion of immersed hypersurfaces driven by surface diffusion flow and give anlower bound on the life span of a smooth immersed solution, which depends only on how muchthe curvature of the initial surface is concentrated in space. 展开更多
关键词 Surface diffusion flow Mean curvature Second fundamental form Fourth order equation
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The Extension of the H^k Mean Curvature Flow in Riemannian Manifolds
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作者 Hongbing QIU Yunhua YE Anqiang ZHU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2014年第2期191-208,共18页
In this paper,the authors consider a family of smooth immersions Ft : Mn→Nn+1of closed hypersurfaces in Riemannian manifold Nn+1with bounded geometry,moving by the Hkmean curvature flow.The authors show that if the s... In this paper,the authors consider a family of smooth immersions Ft : Mn→Nn+1of closed hypersurfaces in Riemannian manifold Nn+1with bounded geometry,moving by the Hkmean curvature flow.The authors show that if the second fundamental form stays bounded from below,then the Hkmean curvature flow solution with finite total mean curvature on a finite time interval [0,Tmax)can be extended over Tmax.This result generalizes the extension theorems in the paper of Li(see "On an extension of the Hkmean curvature flow,Sci.China Math.,55,2012,99–118"). 展开更多
关键词 Hk mean curvature flow Riemannian manifold Sobolev type inequality Moser iteration
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