The Semi-linear Torsional Rigidity on a Complete Riemannian Two-Manifold

2011/04/23 by Jie Xiao, Xiao, Jie
Mathematics · #31A30 #53A05 #53A30 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1104.4562

openalex publication_date 2011/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note is concerned with some essential properties (optimal isoperimetry, first variation, and monotonicity formula) of the so-called [0,1)\niγ-torsional rigidity T_γ,g on a complete Riemannian two-manifold (\mathbb M²,g). Even in the special case of \mathbb R², major results are new.

Citations

• Isoperimetric inequalities and variations on Schwarz's lemma
• Geometric versions of Schwarz’s lemma for quasiregular mappings

Related

• Maximizing torsional rigidity on Riemannian manifolds
• Torsional Rigidity on Compact Riemannian Manifolds with lower Ricci Curvature Bounds
• Heat content, torsional rigidity and generalized Hardy inequalities for complete Riemannian manifolds
• Torsional rigidity of submanifolds with controlled geometry
• Evolution of the Torsional Rigidity under Geometric Flows