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

Jie Xiao

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arXiv · 1104.4562

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

Jie Xiao

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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.

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BibTeX RIS

Jie Xiao. 2011-04-23. The Semi-linear Torsional Rigidity on a Complete Riemannian Two-Manifold. https://arxiv.org/abs/1104.4562

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