A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper solves part of a problem by constructing surfaces with specific curvature and singularities.
Smooth solution found for free boundary problem in higher dimensions.
Characterizes minimal surfaces with finite curvature in specific spaces.
No free boundary Möbius bands exist in a 3D ball.
We investigate a problem posed by L. Hauswirth, F. Hélein, and F. Pacard, namely, to characterize all the domains in the plane that admit a "roof function", i.e., a positive harmonic function which solves simultaneously a Dirichlet problem with null boundary data, and a Neumann problem with constant boundary data. Unde…
We study classical solutions to the one-phase free boundary problem in which the free boundary consists of smooth curves and the components of the positive phase are simply-connected. We show that if two components of the free boundary are close, then the solution locally resembles an entire solution discovered by Haus…
Laurent Hauswirth and Harold Rosenberg developed the theory of minimal surfaces with finite total curvature in $\H^2\times\R$. They showed that the total curvature of one such a surface must be a non-negative integer multiple of . The first examples appearing in this context are vertical geodesic planes and Scherk…
Let (M, g, k) be an initial data set for the Einstein equations of general relativity. We prove that there exist solutions of the Plateau problem for marginally outer trapped surfaces (MOTSs) that are stable in the sense of MOTSs. This answers a question of G. Galloway and N. O'Murchadha and is an ingredient in the pro…
This thesis constructs cmc 1/2 surfaces from catenoids, proving convergence and solving boundary value problems.