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.
The paper explores rigidity of hypersurfaces with constant shifted curvature functions in hyperbolic space.
problem Rigidity of hypersurfaces with constant shifted curvature functions in hyperbolic space.
method Characterizations and rigidity investigations for hypersurfaces with constant weighted shifted mean curvatures or ratios.
result Rigidity results for hypersurfaces with constant linear combinations of weighted shifted mean curvatures and radially symmetric shifted mean curvatures.
We prove rigidity of any properly immersed noncompact Lagrangian shrinker with single valued Lagrangian angle for Lagrangian mean curvature flows. Our pointwise approach also provides an ele- mentary proof to the known rigidity results for graphical and almost graphical shrinkers of mean curvature flows.
Self-shrinkers model singularities of the mean curvature flow; they are defined as the special solutions that contract homothetically under the flow. Colding-Ilmanen-Minicozzi showed that cylindrical self-shrinkers are rigid in a strong sense - that is, any self-shrinker that is mean convex with uniformly bounded curva…
The paper establishes curvature inequalities and rigidity results for CMC and STCMC surfaces in Riemannian and Lorentzian geometry.
problem Curvature inequalities and rigidity for surfaces with constant mean curvature and spacetime constant mean curvature.
method Analysis of curvature inequalities and rigidity results for surfaces in both Riemannian and Lorentzian settings, using stability conditions and extrinsic curvature sign conditions.
result Sharp inequality for spacetime constant mean curvature surfaces and rigidity for the equality case.
Study shows critical width for rigidity of equatorial zones on spheres.
problem Mean curvature rigidity of equatorial zones on spheres.
method Used tangency principle and trap-slice lemma for strong rigidity, and constructed nontrivial perturbations using Delaunay surfaces for non-rigidity.
result Critical width exists for rigidity, beyond which zones are non-rigid.
In this paper, we first investigate several rigidity problems for hypersurfaces in the warped product manifolds with constant linear combinations of higher order mean curvatures as well as "weighted'' mean curvatures, which extend the work \cite{Mon, Brendle,BE} considering constant mean curvature functions. Secondly, …
In this paper we obtain rigidity results and obstructions on the topology at infinity of translating solitons of the mean curvature flow in the Euclidean space. Our approach relies on the theory of f-minimal hypersurfaces.
Study of prescribing scalar curvature and mean curvature on compact manifolds with boundary.
problem Prescribing scalar curvature and mean curvature on compact manifolds with boundary.
method Introducing singular metrics inspired by previous work on closed manifolds, proving rigidity results for flat manifolds with totally geodesic boundary.
result Generic scalar-flat manifolds with minimal boundary can have scalar curvature and mean curvature prescribed simultaneously.
The article proves a Poincaré inequality for hypersurfaces and applies it to rigidity results.
problem Proving rigidity results for hypersurfaces under curvature constraints.
method Using a divergence formula for symmetric endomorphisms, the article deduces a Poincaré type inequality and applies it to higher-order mean curvature of hypersurfaces.
result The article proves several rigidity results for complete r-minimal hypersurfaces.
The study proves a new inequality and formula for manifolds with non-negative Ricci curvature.
problem Proving a sharp mean value inequality for non-negative superharmonic functions.
method Develops a new sharp mean value inequality and an explicit formula for weighted scalar curvature.
result The new inequality removes the radius restriction of Schoen-Yau's result and provides an explicit formula for integral of weighted scalar curvature.
We study the rigidity of complete, embedded constant mean curvature surfaces in R^3. Among other things, we prove that when such a surface has finite genus, then intrinsic isometries of the surface extend to isometries of R^3 or its isometry group contains an index two subgroup of isometries that extend.