63 research outputs found
Translating solitons of mean curvature flow of noncompact spacelike hypersurfaces in Minkowski space
In this paper, we study the existence, uniqueness and asymptotic behavior of
rotationally symmetric translating solitons of the mean curvature flow in
Minkowski space. We also study the asymptotic behavior and the strict convexity
of general solitons of such flows.Comment: 16page
The Anisotropic Convexity of Domains and the Boundary Estimate for Two Monge-Amp\`ere Equations
We study the exact effect of the anisotropic convexity of domains on the
boundary estimate for two Monge-Amp\`ere Equations: one is singular which is
from the proper affine hyperspheres with constant mean curvature; the other is
degenerate which is from the Monge-Amp\`ere eigenvalue problem. As a result, we
obtain the sharp boundary boundary estimates and the optimal global H\"older
regularity for the two equations
A priori estimates and existence of solutions to the prescribed centroaffine curvature problem
In this paper we study the prescribed centroaffine curvature problem in the Euclidean space RāæāŗĀ¹. This problem is equivalent to solving a MongeāAmpĆØre equation on the unit sphere. It corresponds to the critical case of the BlaschkeāSantalĆ³ inequality. By approximation from the subcritical case, and using an obstruction condition and a blow-up analysis, we obtain sufficient conditions for the a priori estimates, and the existence of solutions up to a Lagrange multiplier
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