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Displaying 141 – 153 of 153

Type-II singularities of two-convex immersed mean curvature flow

Theodora Bourni, Mat Langford (2016)

Geometric Flows

We show that any strictly mean convex translator of dimension n ≥ 3 which admits a cylindrical estimate and a corresponding gradient estimate is rotationally symmetric. As a consequence, we deduce that any translating solution of the mean curvature flow which arises as a blow-up limit of a two-convex mean curvature flow of compact immersed hypersurfaces of dimension n ≥ 3 is rotationally symmetric. The proof is rather robust, and applies to a more general class of translator equations. As a particular...

Über die Stetigkeit teilweise freier Minimalflächen.

Gerhard Dziuk (1981)

Manuscripta mathematica

Un teorema sulle correnti intere a supporto non compatto

Maurizio Chicco (1969)

Rendiconti del Seminario Matematico della Università di Padova

Uniform rectifiability and singular sets

Guy David, Stephen Semmes (1996)

Annales de l'I.H.P. Analyse non linéaire

Variational approximation of a functional of Mumford–Shah type in codimension higher than one

Francesco Ghiraldin (2014)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we consider a new kind of Mumford–Shah functional E(u, Ω) for maps u : ℝm → ℝn with m ≥ n. The most important novelty is that the energy features a singular set Su of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy E(u, Ω) via Γ −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L. Ambrosio and V.M. Tortorelli,...

Variations of additive functions

Zoltán Buczolich, Washek Frank Pfeffer (1997)

Czechoslovak Mathematical Journal

We study the relationship between derivates and variational measures of additive functions defined on families of figures or bounded sets of finite perimeter. Our results, valid in all dimensions, include a generalization of Ward’s theorem, a necessary and sufficient condition for derivability, and full descriptive definitions of certain conditionally convergent integrals.

Volumes transverses aux feuilletages définissables dans des structures o-minimales.

F. Chazal, J.M. Lion (2003)

Publicacions Matemàtiques

Vortex rings for the Gross-Pitaevskii equation

Fabrice Bethuel, G. Orlandi, Didier Smets (2004)

Journal of the European Mathematical Society

We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross–Pitaevskii (GP) equation in dimension $N \geq 3$ . We also extend the asymptotic analysis of the free field Ginzburg–Landau equation to a larger class of equations, including the Ginzburg–Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if $N = 3$ ).

Weak and strong density results for the Dirichlet energy

Mariano Giaquinta, Domenico Mucci (2004)

Journal of the European Mathematical Society

Let $𝒴$ be a smooth oriented Riemannian manifold which is compact, connected, without boundary and with second homology group without torsion. In this paper we characterize the sequential weak closure of smooth graphs in $B^{n} \times 𝒴$ with equibounded Dirichlet energies, $B^{n}$ being the unit ball in $ℝ^{n}$ . More precisely, weak limits of graphs of smooth maps $u_{k} : B^{n} \to 𝒴$ with equibounded Dirichlet integral give rise to elements of the space ${cart}^{2, 1} (B^{n} \times 𝒴)$ (cf. [4], [5], [6]). In this paper we prove that every element $T$ in ${cart}^{2, 1} (B^{n} \times 𝒴)$ is the weak limit...

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