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math.DG2011
On the -Liouville property of stochastically incomplete manifolds
G. Pacelli Bessa, Stefano Pigola, Alberto G. Setti
A classical result by Alexander Grigor'yan states that on a stochastically complete manifold the non-negative superharmonic -functions are necessarily constant. In this paper…
math.DG2011
Spectral and stochastic properties of the -Laplacian, solutions of PDE's at infinity, and geometric applications
G. Pacelli Bessa, Stefano Pigola, Alberto G. Setti
The aim of this paper is to suggest a new viewpoint to study qualitative properties of solutions of semilinear elliptic PDE's defined outside a compact set. The relevant tools come…