An inequality for length and volume in the complex projective plane

Mikhail G. Katz

doi:https://doi.org/10.1007/s10711-020-00567-x

An inequality for length and volume in the complex projective plane

Mikhail G. Katz

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a new inequality relating volume to length of closed geodesics on area minimizers for generic metrics on the complex projective plane. We exploit recent regularity results for area minimizers by Moore and White, and the Kronheimer–Mrowka proof of the Thom conjecture.

Original language	English
Pages (from-to)	49-56
Number of pages	8
Journal	Geometriae Dedicata
Volume	213
Issue number	1
DOIs	https://doi.org/10.1007/s10711-020-00567-x
State	Published - Aug 2021

Keywords

Closed geodesics
Croke–Rotman inequality
Gromov’s stable systolic inequality for complex projective space
Kronheimer–Mrowka theorem
Minimal surface
Regularity
Systole

All Science Journal Classification (ASJC) codes

Geometry and Topology

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https://doi.org/10.1007/s10711-020-00567-x

Cite this

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title = "An inequality for length and volume in the complex projective plane",

abstract = "We prove a new inequality relating volume to length of closed geodesics on area minimizers for generic metrics on the complex projective plane. We exploit recent regularity results for area minimizers by Moore and White, and the Kronheimer–Mrowka proof of the Thom conjecture.",

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KW - Croke–Rotman inequality

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KW - Kronheimer–Mrowka theorem

KW - Minimal surface

KW - Regularity

KW - Systole

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An inequality for length and volume in the complex projective plane

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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