Short loops in surfaces with a circle boundary component

2016/02/02 by Panos Papasoglu, Papasoglu, Panos
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematics and Applications #math.DG

paper · pdf · doi:10.48550/arxiv.1602.00854

5 pages

arxiv created 2016/02/02 · openalex publication_date 2016/02/02 · arxiv updated 2016/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is a classical theorem of Loewner that the systole of a Riemannian torus can be bounded in terms of its area. We answer a question of a similar flavor of Robert Young showing that if T is a Riemannian 2-torus with boundary in \mathbb R ⁿ, such that the boundary curve is a standard unit circle, then the length of the shortest non-contractible loop in T is bounded in terms of the area of T.

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