An inequality for length and volume in the complex projective plane

An inequality for length and volume in the complex projective plane

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.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Geometriae dedicata 2021-08, Vol.213 (1), p.49-56
1. Verfasser: Katz, Mikhail G.
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Geodesy
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-020-00567-x