73 citations · 142 across the 37 of their papers we have counts for
4 papers · 1 filter
Degree Theory of Immersed Hypersurfaces
Harold Rosenberg, Graham Smith
We develop a degree theory for compact immersed hypersurfaces of prescribed -curvature immersed in a compact, orientable Riemannian manifold, where is any elliptic curvature…
The Plateau problem for convex curvature functions
Graham Smith
We present a novel and comprehensive approach to the study of the parametric Plateau problem for locally strictly convex (LSC) hypersurfaces of prescribed curvature for general con…
The non-linear Plateau problem in non-positively curved manifolds
Graham Smith
Using the Perron method, we prove the existence of hypersurfaces of prescribed special Lagrangian curvature with prescribed boundary inside complete Riemannian manifolds of non-pos…
Compactness for immersions of prescribed Gaussian curvature II - geometric aspects
Graham Smith
We develop a compactness result near the boundary for families of locally convex immersions. We also develop a mod 2 degree theory for immersion of constant (and prescribed) Gaussi…