Li Ma, Vicente Miquel
Published 2020-12-24Version 1
In this paper, we prove that the infimum of the mean curvature is zero for a translating solitons of hypersurface in $\re^{n+k}$. We give some conditions under which a complete hypersurface translating soliton is stable. We show that if the norm of its mean curvature is less than one, then the weighted volume may have exponent growth. We also study the Dirichlet problem for graphic translating solitons in higher codimensions.
Nonlinear evolution by mean curvature and isoperimetric inequalities
On the Dirichlet problem at infinity on three-manifolds of negative curvature
Sobolev spaces of maps and the Dirichlet problem for harmonic maps
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