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Generalized solutions to the Dirichlet problem of translating mean curvature equ ...

来源:复旦大学数学科学学院 | 2019-03-04 | 发布:经管之家

报告题目: Generalized solutions to the Dirichlet problem of translating mean curvature equations报 告 人:周恒宇报告人所在单位:重庆大学报告日期:2019-03-13 星期三报告时间:14:00-15:00报告地点:光华楼东主楼1801报告摘要:
In this talk we discuss the Dirichlet problem of translating mean curvature equations in Riemannian manifolds with dimension n. Imitating an idea of Miranda-Giusti, we define a new conformal area functionaland a generalized solution to this Dirichlet problem. The existence of generalized solutions to this problem on bounded Lipschitz domains is established. If the domain is mean convex and bounded with C^2 boundary, Its closure does not contain any closed minimal hyper surface except a singular set with its Haudorff dimension at most n-7 and the boundary data is continuous, the generalized solution is the desirable classical smooth solution. The non-minimal condition could not be removed in general.

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