4 papers
An alternative solvability criterion for the Dirichlet problem for the minimal surface equation and an application to the mean curvature flow
Ari J. Aiolfi, Giovanni da Silva Nunes, Jaime Ripoll +2
We propose an alternative condition for the solvability of the Dirichlet problem for the minimal surface equation that applies to non-mean convex domains. We introduce a structural…
The Dirichlet problem for the minimal hypersurface equation with Lipschitz continuous boundary data on domains of a Riemannian manifold
Ari J. Aiolfi, Giovanni Nunes, Lisandra Sauer +1
Given a C2-domain with compact boundary in an arbitrary complete Riemannian manifold, we search for smallness conditions on the boundary data for which the Dirichlet problem for th…
On the Dirichlet problem for the CMC graph equation on multiply connected domains of a Riemannian manifold
Ari J. Aiolfi, Giovanni S. Nunes, Lisandra O. Sauer +1
We establish existence and uniqueness of compact graphs of constant mean curvature in MxR over bounded multiply connected domains of Mx{0} with boundary lying in two parallel horiz…
Some existence results to the Dirichlet problem for the minimal hypersurface equation on non mean convex domains of a Riemannian manifold
Ari Aiolfi, Jaime Ripoll, Marc Soret
We prove the existence of minimal hypersurfaces for the Dirichlet that extends a similar result of Jenkins and Serrin in Euclidean Space to Riemannian ambient manifolds