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

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