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Special Curves in Engineering. Surfaces Generated by the Logarithmic Spiral
Modelling in Civil Environmental Engineering, 2022 The logarithmic spiral is one of the most known curves with applications in engineering. We consider product of the logarithmic spiral with a real line and tensor product of two logarithmic spirals and investigate their minimality or flatness.
Broscăţeanu Ștefan Cezar
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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
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Existence of mean curvature flow singularities with bounded mean curvature
Duke Mathematical Journal, 2023 44 pages, comments ...
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On the evolution by fractional mean curvature [PDF]
Communications in Analysis and Geometry, 2019 In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric quantities that yield preservation of certain quantities (such as positive ...
Sáez, Mariel, Valdinoci, Enrico
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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
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Stability of helicoidal surfaces with constant mean curvature
International Journal of Mathematics for Industry, 2020 Motivated by an experimental result on the shape of liquid water supported by a small stainless helical wire, we find a class of stable helicoidal convex surfaces with constant mean curvature whose boundary consists of a single helix and two short arcs.
Yuta Hatakeyama, Miyuki Koiso
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Preconditioned augmented Lagrangian method for mean curvature image deblurring
AIMS Mathematics, 2022 Image deblurring models with a mean curvature functional has been widely used to preserve edges and remove the staircase effect in the resulting images. However, the Euler-Lagrange equations of a mean curvature model can be used to solve fourth-order non-
Shahbaz Ahmad +6 more
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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
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On the mean curvature of submanifolds with nullity [PDF]
Annals of Global Analysis and Geometry, 2020 In this paper, we investigate geometric conditions for isometric immersions with positive index of relative nullity to be cylinders. There is an abundance of noncylindrical $n$-dimensional minimal submanifolds with index of relative nullity $n-2$, fully described by Dajczer and Florit \cite{DF2} in terms of a certain class of elliptic surfaces. Opposed
A. E. Kanellopoulou, Th. Vlachos
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Lietuvos Matematikos Rinkinys, 2010 In this article we generalize some classical formulas for curvatures of hypersurfaces in the n-dimensional Euclidean space using the homogeneous formulas.
Kazimieras Navickis
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