Jean-Baptiste Casteras

Convexity at infinity in Cartan–Hadamard manifolds and applications to the asymptotic Dirichlet and Plateau problems

We study the asymptotic Dirichlet and Plateau problems on Cartan–Hadamard manifolds satisfying the so-called strict convexity (abbr. SC) condition. The main part of the paper consists in studying the SC condition on a manifold whose sectional curvatures are bounded from above and below by certain functions depending on the distance to a fixed point. In particular, we are able to verify the SC condition on manifolds whose curvature lower bound can go to

ASYMPTOTIC DIRICHLET PROBLEM FOR A-HARMONIC AND MINIMAL GRAPH EQUATIONS IN CARTAN-HADAMARD MANIFOLDS

-\infty

Orbitally Stable Standing Waves of a Mixed Dispersion Nonlinear Schrödinger Equation

-∞ and upper bound to 0 simultaneously at certain rates, or on some manifolds whose sectional curvatures go to

On asymptotic plateau’s problem for CMC hypersurfaces on rank 1 symmetric spaces of noncompact type

-\infty

A mean field type flow part I: compactness of solutions to a perturbed mean field type equation

-∞ faster than any prescribed rate. These improve previous results of Anderson, Borbély, and Ripoll and Telichevsky. We then solve the asymptotic Plateau problem for locally rectifiable currents with