Evolving compact locally convex curves and convex hypersurfaces
DOI10.1007/s00229-021-01278-7zbMath1486.52002OpenAlexW3130116063MaRDI QIDQ2066296
Publication date: 14 January 2022
Published in: Manuscripta Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00229-021-01278-7
Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Initial value problems for second-order parabolic equations (35K15) Convex sets in (2) dimensions (including convex curves) (52A10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Euclidean geometries (general) and generalizations (51M05)
Cites Work
- Flow by mean curvature of convex surfaces into spheres
- On the formation of singularities in the curve shortening flow
- A representation formula for the inverse harmonic mean curvature flow
- On a non-local perimeter-preserving curve evolution problem for convex plane curves
- Evolving a convex closed curve to another one via a length-preserving linear flow
- Deforming convex hypersurfaces by the \(n\)th root of the Gaussian curvature
- Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature
- The normalized curve shortening flow and homothetic solutions
- The heat equation shrinking convex plane curves
- The mixed volume preserving mean curvature flow
- Convexity estimates for mean curvature flow and singularities of mean convex surfaces
- Entropy and a convergence theorem for Gauss curvature flow in high dimension
- Asymptotic behavior of flows by powers of the Gaussian curvature
- Mean curvature flow with surgery of mean convex surfaces in three-manifolds
- Gauss curvature flow: The fate of the rolling stones
- Three-manifolds with positive Ricci curvature
- Length-preserving evolution of immersed closed curves and the isoperimetric inequality
- The surface area preserving mean curvature flow
- The volume preserving mean curvature flow.
- Evolving convex surfaces to constant width ones
- Evolution of non-simple closed curves in the area-preserving curvature flow
- Evolution of highly symmetric curves under the shrinking curvature flow
- Volume-preserving mean curvature flow of hypersurfaces in space forms
- A characterization of convex hypersurfaces in Hadamard manifolds
- Mean curvature flow with surgery of mean convex surfaces in \(\mathbb R^3\)
This page was built for publication: Evolving compact locally convex curves and convex hypersurfaces