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

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

2011-04-23

arxiv.org/abs/1104.4562v1

Mathematics

Differential Geometry

11 pages

Scientific paper

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.

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