A survey of closed self-shrinkers with symmetry (Q1743244)

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English	A survey of closed self-shrinkers with symmetry	scientific article

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scholarly article

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A survey of closed self-shrinkers with symmetry (English)

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Xuan Hien Nguyen

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Results in Mathematics

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publication date

13 April 2018

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full work available at URL

https://arxiv.org/abs/1708.09113

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zbMATH Keywords

rotational symmetry

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MaRDI profile type

MaRDI publication profile

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The normalized curve shortening flow and homothetic solutions

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Constant mean curvature tori in terms of elliptic functions.

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A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)

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\(O(m) \times O(n)\)-invariant minimal hypersurfaces in \(\mathbb R^{m+n}\)

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A comparison theorem for the isoperimetric profile under curve-shortening flow

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Curvature bound for curve shortening flow via distance comparison and a direct proof of Grayson's theorem

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Parabolic equations for curves on surfaces. I: Curves with \(p\)-integrable curvature

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Parabolic equations for curves on surfaces. II: Intersections, blow-up and generalized solutions

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Minimal cones and the Bernstein problem

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Embedded self-similar shrinkers of genus 0

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1-dimensional solutions of the \(\lambda \)-self shrinkers

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Mean curvature flow

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On De Giorgi's conjecture in dimension \(N\geq 9\)

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An immersed 𝑆² self-shrinker

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Mean curvature flow of entire graphs evolving away from the heat flow

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Shrinking doughnuts via variational methods

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Immersed self-shrinkers

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Regularity theory for mean curvature flow

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A stable manifold theorem for the curve shortening equation

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Uniqueness Theorems for Free Boundary Minimal Disks in Space Forms

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The heat equation shrinking convex plane curves

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Isoperimetric inequalities for submanifolds. Jellett-Minkowski's formula revisited

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The heat equation shrinks embedded plane curves to round points

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Self-similar solutions to the curve shortening flow

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Self-similar solutions to the mean curvature flow in the Minkowski plane \(\mathbb{R}^{1,1}\)

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Monotonicity formulas for parabolic flows on manifolds

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Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern.

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The computer-aided discovery of new embedded minimal surfaces

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New examples of constant mean curvature immersions of (2k-1)-spheres into euclidean 2k-space

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Generalized rotational hypersurfaces of constant mean curvature in the euclidean spaces. I

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Some integral formulas for closed hypersurfaces in Riemannian space

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Some integral formulas for closed hypersurfaces

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Flow by mean curvature of convex surfaces into spheres

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Asymptotic behavior for singularities of the mean curvature flow

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A distance comparison principle for evolving curves

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Self-shrinkers with a rotational symmetry

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Mean curvature self-shrinkers of high genus: non-compact examples

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Weierstrass formula for surfaces of prescribed mean curvature

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An extension of Hsiung-Minkowski formulas and some applications

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The unknottedness of minimal embeddings

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A note on Grayson's theorem

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Unicity of constant mean curvature hypersurfaces in some riemannian manifolds

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On the Topological Rigidity of Compact Self-shrinkers in ℝ3

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Counterexample to a conjecture of H. Hopf

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Identifiers

zbMATH Open document ID

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10.1007/s00025-018-0763-3

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:1743244

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