Results 11 to 20 of about 5,400,024 (317)
A convergent evolving finite element algorithm for mean curvature flow of closed surfaces [PDF]
Numerische Mathematik, 2018 A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the discrete surface ...
Bal'azs Kov'acs, Buyang Li, C. Lubich
semanticscholar +1 more source
Existence of hypersurfaces with prescribed mean curvature I – generic min-max [PDF]
Cambridge Journal of Mathematics, 2018 We prove that, for a generic set of smooth prescription functions $h$ on a closed ambient manifold, there always exists a nontrivial, smooth, closed hypersurface of prescribed mean curvature $h$.
Xin Zhou, Jonathan J. Zhu
semanticscholar +1 more source
Hyperbolic mean curvature flow [PDF]
Journal of Differential Equations, 2009 In this paper we introduce the hyperbolic mean curvature flow and prove that the corresponding system of partial differential equations are strictly hyperbolic, and based on this, we show that this flow admits a unique short-time smooth solution and possesses the nonlinear stability defined on the Euclidean space with dimension larger than 4. We derive
Chun-Lei He, Kefeng Liu, Dexing Kong
openaire +2 more sources
Scherk-like translators for mean curvature flow [PDF]
Journal of differential geometry, 2019 We prove existence and uniqueness for a two-parameter family of translators for mean curvature flow. We get additional examples by taking limits at the boundary of the parameter space.
D. Hoffman, F. Mart'in, B. White
semanticscholar +1 more source
Curvature estimates for constant mean curvature surfaces [PDF]
Duke Mathematical Journal, 2019 We have separated the original paper into two parts. This new posting is the first part which is self-contained and deals with extrinsic curvature estimates for embedded nonzero constant mean curvature disks.
H. Meeks III, William +1 more
openaire +6 more sources
Notes on Translating Solitons for Mean Curvature Flow [PDF]
Minimal Surfaces: Integrable Systems and Visualisation, 2019 The purpose of these notes is to provide an introduction to those who want to learn more about translating solitons for the mean curvature flow in $\mathbb{R}^3$, particularly those which are complete graphs over domains in $\mathbb{R}^2$.
D. Hoffman +3 more
semanticscholar +1 more source
Journal of the European Mathematical Society, 2012 We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence.
Dai, Qiuyi +2 more
openaire +5 more sources
Curvature estimates for surfaces with bounded mean curvature [PDF]
Transactions of the American Mathematical Society, 2012 Estimates for the norm of the second fundamental form, | A | |A| , play a crucial role in studying the geometry of surfaces in R 3 \mathbb {R}^3 . In fact, when | A |
Bourni, Theodora, Tinaglia, Giuseppe
openaire +7 more sources
Overdetermined problems and constant mean curvature surfaces in cones [PDF]
Revista matemática iberoamericana, 2018 We consider a partially overdetermined problem in a sector-like domain $\Omega$ in a cone $\Sigma$ in $\mathbb{R}^N$, $N\geq 2$, and prove a rigidity result of Serrin type by showing that the existence of a solution implies that $\Omega$ is a spherical ...
F. Pacella, G. Tralli
semanticscholar +1 more source
Forced hyperbolic mean curvature flow [PDF]
, 2012 In this paper, we investigate two hyperbolic flows obtained by adding forcing terms in direction of the position vector to the hyperbolic mean curvature flows in \cite{klw,hdl}.
Mao, Jing
core +1 more source