Nonpositively Curved Surfaces are Loewner

Mikhail G. Katz; Stéphane Sabourau

doi:10.1007/s12220-024-01732-4

Nonpositively Curved Surfaces are Loewner

Mikhail G. Katz, Stéphane Sabourau

Department of Mathematics

Bar-Ilan University

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

Abstract

We show that every closed nonpositively curved surface satisfies Loewner’s systolic inequality. The proof relies on a combination of the Gauss–Bonnet formula with an averaging argument using the invariance of the Liouville measure under the geodesic flow. This enables us to find a disk with large total curvature around its center yielding a large area.

Original language	English
Article number	291
Journal	Journal of Geometric Analysis
Volume	34
Issue number	9
DOIs	https://doi.org/10.1007/s12220-024-01732-4
State	Published - Sep 2024

Keywords

Liouville measure
Nonpositively curved surface
Primary 53C20
Secondary 53C23
Systole
Systolic inequality

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1007/s12220-024-01732-4

Cite this

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abstract = "We show that every closed nonpositively curved surface satisfies Loewner{\textquoteright}s systolic inequality. The proof relies on a combination of the Gauss–Bonnet formula with an averaging argument using the invariance of the Liouville measure under the geodesic flow. This enables us to find a disk with large total curvature around its center yielding a large area.",

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AB - We show that every closed nonpositively curved surface satisfies Loewner’s systolic inequality. The proof relies on a combination of the Gauss–Bonnet formula with an averaging argument using the invariance of the Liouville measure under the geodesic flow. This enables us to find a disk with large total curvature around its center yielding a large area.

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KW - Nonpositively curved surface

KW - Primary 53C20

KW - Secondary 53C23

KW - Systole

KW - Systolic inequality

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DO - 10.1007/s12220-024-01732-4

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ER -

Nonpositively Curved Surfaces are Loewner

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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