Stokes' theorem, volume growth and parabolicity

2010/05/31 by Daniele Valtorta, Giona Veronelli
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows #Laplace operator #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Partial Differential Equations #Physics #Pure mathematics #Quantum mechanics #Type (biology) #Uniqueness #Work (physics) #math.DG #msc:31C12 #msc:53C43

paper · pdf · doi:10.2748/tmj/1318338948

published as Tohoku Math. J. (2) Volume 63, Number 3 (2011), 397-412 · 15 pages. Corrected typos. Accepted for publication in Tohoku Mathematical Journal

openalex publication_date 2011/01/01 · arxiv created 2011/05/25 · arxiv updated 2012/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present some new Stokes' type theorems on complete non-compact manifolds that extend, in different directions, previous works 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.

Citations

• Vanishing and Finiteness Results in Geometric Analysis
• The connectivity at infinity of a manifold and L^q,p-Sobolev inequalities
• Mappings minimizing the L p norm of the gradient
• Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative ricci curvature
• The structure of stable minimal hypersurfaces in Rⁿ