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Stokes theorem, volume growth and parabolicity. (English) Zbl 1232.26011

Summary: 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.

MSC:

26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
31C45 Other generalizations (nonlinear potential theory, etc.)
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