ICTP Math Associates Seminar (Zoom Meeting) - Thursday 18 February at 14:00 (Leandro da Freitas Pessoa)

[ICTP Math Section]

ICTP Math Associates Seminar


Thursday 18 February, at 14:00, Central European Time



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Speaker: Leandro da Freitas Pessoa (UFPI)


Title: Detecting the completeness of a Finsler manifold via potential 
theory for its infinity Laplacian


Abstract: In this talk we will present some potential-theoretic aspects 
of the eikonal and infinity Laplace operator on a Finsler manifold M. 
Our main result shows that the forward completeness of M can be detected 
in terms of Liouville properties and maximum principles at infinity for 
subsolutions of suitable in homogeneous inequalities. Also, an 
∞-capacity criterion and a viscosity version of Ekeland principle are 
proved to be equivalent to the forward completeness of M. Part of the 
proof hinges on a new boundary-to-interior Lipschitz estimate for 
solutions of an inhomogeneous equation for the infinity Laplacian on 
compact sets, that implies a uniform Lipschitz estimate for certain 
entire, bounded solutions without requiring the completeness of M.