On minimal higher genus fillings

2022/02/03 by Gregory R. Chambers, Chambers, Gregory R.
Mathematics · #53C23 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2202.01342

openalex publication_date 2022/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we prove that if (M,g) is a genus G orientable surface with a single boundary component S¹, and if (D,g₀) is a disc such that interior points are connected by unique geodesics and d_(D,g0)(x,y) ≥ d_(M,g)(x,y) for all x,y ∈ ∂ M = ∂ D, then (1 + \frac2 Gπ) \textrmArea(M,g) ≥ \textrmArea(D,g₀).

Related

• Filling systems of maximum size
• Filling systems on surfaces
• Filling area conjecture and ovalless real hyperelliptic surfaces
• A note on minimal surfaces with bounded index
• Filling with separating curves