Results 21 to 30 of about 265,786 (329)
Multi-Reconstruction from Points Cloud by Using a Modified Vector-Valued Allen–Cahn Equation
Mathematics, 2021 The Poisson surface reconstruction algorithm has become a very popular tool of reconstruction from point clouds. If we reconstruct each region separately in the process of multi-reconstruction, then the reconstructed objects may overlap with each other ...
Jin Wang, Zhengyuan Shi
doaj +1 more source
Universality in mean curvature flow neckpinches [PDF]
, 2014 We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is $C^3$-close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically
Gang, Zhou, Knopf, Dan
core +2 more sources
Formal asymptotic expansions for symmetric ancient ovalsin mean curvature flow
Networks and Heterogeneous Media, 2013 We provide formal matched asymptotic expansions for ancient convex solutions to MCF. The formal analysis leading to the solutions is analogous to that for the generic MCF neck pinch in [1].
Sigurd Angenent
doaj +1 more source
A survey on Inverse mean curvature flow in ROSSes
Complex Manifolds, 2017 In this survey we discuss the evolution by inverse mean curvature flow of star-shaped mean convex hypersurfaces in non-compact rank one symmetric spaces.
Pipoli Giuseppe
doaj +1 more source
Existence of mean curvature flow singularities with bounded mean curvature
Duke Mathematical Journal, 2023 44 pages, comments ...
openaire +2 more sources
Hamiltonian mean curvature flow [PDF]
International Journal of Contemporary Mathematical Sciences, 2013 Let ( , ) be a compact Riemann surface with constant curvature c. In this work, we proved that the mean curvature flow of a given Hamiltonian diffeomorphism on provides a smooth path in Ham( ), the group of all Hamiltonian diffeomorphisms of .
Houenou, Djideme F. +1 more
openaire +2 more sources
Mean Convex Mean Curvature Flow with Free Boundary [PDF]
Communications on Pure and Applied Mathematics, 2021 AbstractIn this paper, we generalize White's regularity and structure theory for mean‐convex mean curvature flow [45, 46, 48] to the setting with free boundary. A major new challenge in the free boundary setting is to derive an a priori bound for the ratio between the norm of the second fundamental form and the mean curvature. We establish such a bound
Edelen, Nick +3 more
openaire +3 more sources
A nonlinear partial differential equation for the volume preserving mean curvature flow
Networks and Heterogeneous Media, 2013 We analyze the evolution of multi-dimensional normal graphs overthe unit sphere under volume preserving mean curvature flow andderive a non-linear partial differential equation in polarcoordinates.
Dimitra Antonopoulou, Georgia Karali
doaj +1 more source
Ancient solutions in Lagrangian mean curvature flow
, 2020 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 ...
Lambert, Ben +2 more
core +2 more sources
Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space
Abstract and Applied Analysis, 2014 Let f(x) be a smooth strictly convex solution of det(∂2f/∂xi∂xj)=exp(1/2)∑i=1nxi(∂f/∂xi)-f defined on a domain Ω⊂Rn; then the graph M∇f of ∇f is a space-like self-shrinker of mean curvature flow in Pseudo-Euclidean space Rn2n with the indefinite metric ...
Ruiwei Xu, Linfen Cao
doaj +1 more source