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

Abstract

This note is concerned with some essential properties (optimal isoperimetry, first variation, and monotonicity formula) of the so-called $[0,1)\ni \gamma$-torsional rigidity ${\mathcal{T}}_{\gamma ,\mathsf{g}}$ on a complete Riemannian two-manifold $({\mathbb{M}}^2,\mathsf{g})$. Even in the special case of ${\mathbb{R}}^2$, major results are new.

11 pages

References in corpus (1)

• Isoperimetric inequalities and variations on Schwarz's lemma