Event Details

Conferenciante : Ilkka Holopainen Título: Asimptotic Plateau problem for prescribed mean curvature hypersurfaces
Impartida por: ​Antonio Luis Martínez-Triviño (University of Helsinki)
Abstract: I will talk on a recent joint preprint with Jean-Baptiste Casteras and Jaime Ripoll. We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribed mean curvature in Cartan-Hadamard manifolds \( N\). More precisely, given a suitable subset \(L\) of the asymptotic boundary of \(N\) and a suitable function \(H\) on \(N\), we are able to construct a set of locally finite perimeter whose boundary has generalized mean curvature \(H\) and asymptotic boundary \(L\) provided that \(N\) satisfies the so-called strict convexity condition and that its sectional curvatures are bounded from above by a negative constant. We also obtain a multiplicity result in low dimensions.
14 de mayo de 2019, 12:30, Seminario 1ª planta IEMath-GR