Results 1 to 10 of about 45,772 (118)

Lagrangian mean curvature flow [PDF]

, 2021
Lagrangian mean curvature flow is a powerful tool in modern mathematics with connections to topics in analysis, geometry, topology and mathematical physics.
Lotay, Jason D.
core   +2 more sources

Hyperbolic inverse mean curvature flow [PDF]

, 2020
summary:We prove the short-time existence of the hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of $\mathbb {R}^{n+1}$ ($n\ge 2$) is mean convex and ...
Zhou, Zhe, Mao, Jing, Wu, Chuan-Xi
core   +1 more source

Backward uniqueness for the inverse mean curvature flow

, 2023
In this paper, we prove a backward uniqueness theorem for solutions to the inverse mean curvature flow on a closed manifold. As a consequence, the isometry group of a solution cannot expand within the lifetime of the solution ...
Ho, Pak-tung
core   +1 more source

A model for the behavior of fluid droplets based on mean curvature flow [PDF]

, 2012
The authors of [W. D. Ristenpart et al., Nature, 461 (2009), pp. 377–380] have observed the following remarkable phenomenon during their experiments.
Helmensdorfer, Sebastian
core   +1 more source

On Type-I singularities in Ricci flow [PDF]

, 2011
07.02.13 KB. Accepted version ok to add to Spiral. IP/Sherpa.We define several notions of singular set for Type I Ricci flows and show that they all coincide.
Topping, Peter, Topping, P, Muller, Reto, Enders, J, Enders, Joerg, Müller, R   +5 more
core   +1 more source

A varifold formulation of mean curvature flow with Dirichlet or dynamic boundary conditions [PDF]

, 2018
We consider the sharp interface limit of the Allen-Cahn equation with Dirichlet or dynamic boundary conditions and give a varifold characterization of its limit which is formally a mean curvature flow with Dirichlet or dynamic boundary conditions.
Takasao, Keisuke, Onoue, Fumihiko, Yoshikazu Giga, Keisuke Takasao, Giga, Yoshikazu   +4 more
core   +1 more source

Forced anisotropic mean curvature flow of graphs in relative geometry [PDF]

, 2014
summary:The paper is concerned with the graph formulation of forced anisotropic mean curvature flow in the context of the heteroepitaxial growth of quantum dots. The problem is generalized by including anisotropy by means of Finsler metrics.
Beneš, Michal, Hoang, Dieu Hung
core   +1 more source

Mean curvature flow with generic initial data [PDF]

, 2020
We show that the mean curvature flow of generic closed surfaces in $\mathbb{R}^{3}$ avoids asymptotically conical and non-spherical compact singularities. We also show that the mean curvature flow of generic closed low-entropy hypersurfaces in $\mathbb{R}
Mantoulidis, C, Schulze, F, Chodosh, O, Chodosh, Otis, Schulze, Felix, Mantoulidis, Christos, Choi, K., Chodosh, O., Choi, Kyeongsu, Mantoulidis, C., Choi, K   +10 more
core   +1 more source

Harmonic mean curvature flow and geometric inequalities

, 2021
We employ the harmonic mean curvature flow of strictly convex closed hypersurfaces in hyperbolic space to prove Alexandrov-Fenchel type inequalities relating quermassintegrals to the total curvature, which is the integral of Gaussian curvature on the ...
Hu, Yingxiang, Li, Haizhong, Andrews, Ben   +2 more
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Mean curvature flow in an extended Ricci flow background

, 2023
In this paper, we consider functionals related to mean curvature flow in an ambient space which evolves by an extended Ricci flow from the perspective introduced by Lott when studying a mean curvature flow in a Ricci flow background.
Gomes, José N. V., Hudson, Matheus
core   +1 more source