Stokes' theorem, volume growth and parabolicity
Daniele Valtorta, Giona Veronelli
TL;DR
This paper introduces new Stokes' theorems on complete non-compact manifolds, extending previous results and criteria for p-parabolicity, with applications to p-Laplacian comparison and uniqueness theorems.
Contribution
It develops novel Stokes' type theorems that generalize existing criteria for parabolicity on manifolds, advancing the understanding of geometric analysis.
Findings
New Stokes' theorems for non-compact manifolds
Extension of Kelvin-Nevanlinna-Royden criterion
Applications to p-Laplacian comparison and uniqueness
Abstract
We present some new Stokes' type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications to comparison and uniqueness results involving the p-Laplacian are deduced.
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