The width of embedded circles
-
Lucas Ambrozio
,
Rafael Montezuma
Abstract
We develop a Morse–Lusternik–Schnirelmann theory for the distance between two points of a smoothly embedded circle in a complete Riemannian manifold. This theory suggests very naturally a definition of width that generalises the classical definition of the width of plane curves. Pairs of points of the circle realising the width bound one or more minimising geodesics that intersect the curve in special configurations. When the circle bounds a totally convex disc, we classify the possible configurations under a further geometric condition. We also investigate properties and characterisations of curves that can be regarded as the Riemannian analogues of plane curves of constant width.
Funding source: Conselho Nacional de Desenvolvimento Científico e Tecnológico
Award Identifier / Grant number: 309908/2021-3
Award Identifier / Grant number: 311028/2020.9
Award Identifier / Grant number: SEI-260003/000534/2023
Award Identifier / Grant number: SEI-260003/001527/2023
Funding statement: Lucas Ambrozio is supported by CNPq – Conselho Nacional de Desenvolvimento Científico e Tecnológico (309908/2021-3 – Bolsa PQ) and by FAPERJ – Fundaçao Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (grant SEI-260003/000534/2023 – BOLSA E-26/200.175/2023 and grant SEI-260003/001527/2023 – APQ1 E-26/210.319/2023). Rafael Montezuma is supported by Instituto Serrapilheira grant “New perspectives of the min-max theory for the area functional” and by CNPq – Conselho Nacional de Desenvolvimento Científico e Tecnológico (311028/2020.9 – Bolsa PQ). Roney Santos is supported by Instituto Serrapilheira grant “New perspectives of the min-max theory for the area functional”.
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© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- K-moduli of Fano threefolds and genus four curves
- Conformally covariant boundary operators and sharp higher order CR Sobolev trace inequalities on the Siegel domain and complex ball
- Dynamique analytique sur 𝐙. II : Écart uniforme entre Lattès et conjecture de Bogomolov-Fu-Tschinkel
- Continuous sparse domination and dimensionless weighted estimates for the Bakry–Riesz vector
- Entire hypersurfaces of constant scalar curvature in Minkowski space
- On the singular loci of higher secant varieties of Veronese embeddings
- A proof of Vishik’s nonuniqueness theorem for the forced 2D Euler equation
- The width of embedded circles
Artikel in diesem Heft
- Frontmatter
- K-moduli of Fano threefolds and genus four curves
- Conformally covariant boundary operators and sharp higher order CR Sobolev trace inequalities on the Siegel domain and complex ball
- Dynamique analytique sur 𝐙. II : Écart uniforme entre Lattès et conjecture de Bogomolov-Fu-Tschinkel
- Continuous sparse domination and dimensionless weighted estimates for the Bakry–Riesz vector
- Entire hypersurfaces of constant scalar curvature in Minkowski space
- On the singular loci of higher secant varieties of Veronese embeddings
- A proof of Vishik’s nonuniqueness theorem for the forced 2D Euler equation
- The width of embedded circles
