Tohoku Mathematical Journal
2011

September
SECOND SERIES VOL. 63, NO. 3

Tohoku Math. J.
63 (2011), 397-412

Title STOKES' THEOREM, VOLUME GROWTH AND PARABOLICITY

Author Daniele Valtorta and Giona Veronelli

(Received July 28, 2010, revised January 14, 2011)
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.

2000 Mathematics Subject Classification. Primary 35B05; Secondary 31C45.

Key words and phrases. $p$-parabolicity, Stokes' theorem, Kelvin-Nevanlinna-Royden criterion.

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