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Convexity and the Dirichlet problem of translating mean curvature flows. (English) Zbl 1400.35110
Summary: In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in $$R^{n+1}$$. We study the basic properties, such as positivity preserving property, of the translating mean curvature flow. The Dirichlet problem for the graphical translating mean curvature flow is studied and the global existence of the flow and the convergence property are also considered.

##### MSC:
 35J60 Nonlinear elliptic equations 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 58J05 Elliptic equations on manifolds, general theory
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