l-convex legendre curves and geometric inequalities
Abstract: In this paper we consider ℓ-convex Legendre curves, which are natural generalizations of strictly convex curves. We generalize various optimal geometric inequalities, isoperimetric inequality, Bonnesen’s inequality and Green–Osher inequality, for strictly convex curves to ones for ℓ-convex Legendre curves. Moreover we generalize the inverse curvature curve flow for this class of Legendre curves and prove that it always converges to a compact soliton after rescaling. Unlike in the class of regular curves, there are infinitely many compact solitons, which include circles and astroids
- Location
-
Deutsche Nationalbibliothek Frankfurt am Main
- Extent
-
Online-Ressource
- Language
-
Englisch
- Notes
-
Calculus of variations and partial differential equations. - 62, 4 (2023) , 135, ISSN: 1432-0835
- Classification
-
Mathematik
- Event
-
Veröffentlichung
- (where)
-
Freiburg
- (who)
-
Universität
- (when)
-
2023
- Creator
- DOI
-
10.1007/s00526-023-02480-z
- URN
-
urn:nbn:de:bsz:25-freidok-2358463
- Rights
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
-
14.08.2025, 10:48 AM CEST
Data provider
This object is provided by:
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Li, Mingyan
- Wang, Guofang
- Universität
Time of origin
- 2023
Other Objects (12)
$$\ell $$ ℓ -convex Legendre curves and geometric inequalities
Convex supply curves
Subelliptic geometric Hardy type inequalities on half-spaces and convex domains
Geometric inequalities
From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies
From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies
Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg group
Set characterizations and convex extensions for geometric convex-hull proofs
Set characterizations and convex extensions for geometric convex-hull proofs
Generalized geometrically convex functions and inequalities
HADAMARD INEQUALITIES FOR WRIGHT-CONVEX FUNCTIONS
GEOMETRIC INEQUALITIES FOR PLANE HEDGEHOGS
$$\ell $$ ℓ -convex Legendre curves and geometric inequalities
Convex supply curves
Subelliptic geometric Hardy type inequalities on half-spaces and convex domains
Geometric inequalities
From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies
From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies
Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg group
Set characterizations and convex extensions for geometric convex-hull proofs
Set characterizations and convex extensions for geometric convex-hull proofs
Generalized geometrically convex functions and inequalities
HADAMARD INEQUALITIES FOR WRIGHT-CONVEX FUNCTIONS
GEOMETRIC INEQUALITIES FOR PLANE HEDGEHOGS
$$\ell $$ ℓ -convex Legendre curves and geometric inequalities
Convex supply curves
Subelliptic geometric Hardy type inequalities on half-spaces and convex domains
Geometric inequalities
From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies
From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies
Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg group
Set characterizations and convex extensions for geometric convex-hull proofs
Set characterizations and convex extensions for geometric convex-hull proofs
Generalized geometrically convex functions and inequalities
HADAMARD INEQUALITIES FOR WRIGHT-CONVEX FUNCTIONS