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The fractional mean curvature flow
Bruno Pini Mathematical Analysis Seminar, 2020 In this note, we present some recent results in the study of the fractional mean curvature flow, that is a geometric evolution of the boundary of a set whose speed is given by the fractional mean curvature.
Eleonora Cinti
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On inextensible ruled surfaces generated via a curve derived from a curve with constant torsion
AIMS Mathematics, 2023 If both the arc length and the intrinsic curvature of a curve or surface are preserved, then the flow of the curve or surface is said to be inextensible. The absence of motion-induced strain energy is the physical characteristic of inextensible curve and
Nural Yüksel, Burçin Saltık
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GeoStamp: Detail Transfer Based on Mean Curvature Field
Mathematics, 2022 A shape detail transfer is the process of extracting the geometric details of a source region and transferring it onto a target region. In this paper, we present a simple and effective method, called GeoStamp, for transferring shape details using a ...
Jung-Ho Park +3 more
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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
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On the Minimization of Total Mean Curvature [PDF]
The Journal of Geometric Analysis, 2015 Equipe Equations aux derivees ...
Dalphin, Jeremy +3 more
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Uniqueness of two-convex closed ancient solutions to the mean curvature flow [PDF]
Annals of Mathematics, 2018 In this paper we consider closed non-collapsed ancient solutions to the mean curvature flow ($n \ge 2$) which are uniformly two-convex. We prove that any two such ancient solutions are the same up to translations and scaling.
S. Angenent +2 more
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Gaussian mean curvature flow [PDF]
Journal of Evolution Equations, 2010 10 ...
A. A. Borisenko, Vicente Miquel
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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
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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
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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
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