2,719 research outputs found
Construction of Maximal Hypersurfaces with Boundary Conditions
We construct maximal hypersurfaces with a Neumann boundary condition in
Minkowski space via mean curvature flow. In doing this we give general
conditions for long time existence of the flow with boundary conditions with
assumptions on the curvature of a the Lorentz boundary manifold
Ancient solutions in Lagrangian mean curvature flow
Ancient solutions of Lagrangian mean curvature flow in C^n naturally arise as
Type II blow-ups. In this extended note we give structural and classification
results for such ancient solutions in terms of their blow-down and, motivated
by the Thomas-Yau Conjecture, focus on the almost calibrated case. In
particular, we classify Type II blow-ups of almost calibrated Lagrangian mean
curvature flow when the blow-down is a pair of transverse planes or, when n=2,
a multiplicity two plane. We also show that the Harvey-Lawson Clifford torus
cone in C^3 cannot arise as the blow-down of an almost calibrated Type II
blow-up.Comment: 30 pages, v2: minor typos corrected, accepted in Ann. Sc. Norm.
Super. Pisa Cl. Sc
The inverse mean curvature flow perpendicular to the sphere
We consider the smooth inverse mean curvature flow of strictly convex hypersurfaces with boundary embedded in R n+1 , Rn+1, which are perpendicular to the unit sphere from the inside. We prove that the flow hypersurfaces converge to the embedding of a flat disk in the norm of C 1,β , C1,β, β<1 β<1
Could Multimedia approaches help Remote Sensing Analysis?
International audienceThe paper explores how multimedia approaches used in image understanding tasks could be adapted and used in remote sensing image analysis. Two approaches are investigated: the classical Bag of Visual Words (BoVW) approach and the Deep Learning approach. Tests are performed for the classification of the UC Merced Land Use Dataset which provide better results than the state of the art
A capillary problem for spacelike mean curvature flow in a cone of Minkowski space
Consider a convex cone in three-dimensional Minkowski space which either
contains the lightcone or is contained in it. This work considers mean
curvature flow of a proper spacelike strictly mean convex disc in the cone
which is graphical with respect to its rays. Its boundary is required to have
constant intersection angle with the boundary of the cone. We prove that the
corresponding parabolic boundary value problem for the graph admits a solution
for all time which rescales to a self-similarly expanding solution.Comment: 19 page
Weyl Estimates for spacelike hypersurfaces in de Sitter space
We study the isometric spacelike embedding problem in scaled de Sitter space, and obtain Weyl-type estimates and the corresponding closedness in the space of embeddings
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