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.
Study shows uniqueness of solutions on complex manifolds without requiring solution decay.
This is a revised version (minor changes and a deeper insight in the positive curvature case). We prove some Caccioppoli's inequalities for the traceless part of the second fundamental form of a complete, noncompact, finite index, constant mean curvature hypersurface of a Riemannian manifold, satisfying some curvature …
Smooth approximations near singularities of constant mean curvature surfaces are found.
The study extends removability results for quasiregular curves in Euclidean spaces.
Alternative proofs for various inequalities on Riemannian manifolds.
Establishes interior regularity results for a broad class of two-dimensional nonlinear elliptic systems using a unified abstract framework.
We prove that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves, are two-sided and have multiplicity one. This confirms a conjecture by Marques-Neves. We prove that in a bumpy metric each…
We show that directed minimal cones in (n+1)-dimensional Euclidean space which have at most one singularity are - besides the trivial cases: empty set, whole space - half spaces. Using blow-up techniques, this result can be used to get C^{1,lambda}-regularity for the measure-theoretic boundary of almost minimal Cacciop…
By using a suitable triple cover we show how to possibly model the construction of a minimal surface with positive genus spanning all six edges of a tetrahedron, working in the space of BV functions and interpreting the film as the boundary of a Caccioppoli set in the covering space. After a question raised by R. Hardt…
The paper proves Hardy inequalities on Finsler manifolds using superharmonicity.
Study on liquid-vapor interfaces in stable equilibrium without assuming prior regularity.
The paper proves the existence of hypersurfaces with prescribed mean curvature.
Alternative proof and extension of curvature estimates for minimal immersions.
In a previous paper we developed a regularity and compactness theory in Euclidean ambient spaces for codimension 1 weakly stable CMC integral varifolds satisfying two (necessary) structural conditions. Here we generalize this theory to the setting where the mean curvature (of the regular part of the varifold) is prescr…