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.
New Einstein metrics found on a 10-dimensional sphere.
In the 1950's Hopf gave examples of non-round convex 2-spheres in Euclidean 3-space with rotational symmetry that satisfy a linear relationship between their principal curvatures. In this paper we investigate conditions under which evolving a smooth rotationally symmetric sphere by a linear combination of its radii of …
We establish a connection between capillary floating in neutral equilibrium and the billiard ball problem. This allows us to reduce the question of floating in neutral equilibrium at any orientation with a prescribed contact angle for infinite homogeneous cylinders to a question about billiard caustics for their orthog…
Researchers prove existence of a special Einstein metric on a 12-dimensional sphere.
We establish an explicit expression for the smallest non-zero eigenvalue of the Laplace--Beltrami operator on every homogeneous metric on the 3-sphere, or equivalently, on SU(2) endowed with left-invariant metric. For the subfamily of 3-dimensional Berger spheres, we obtain a full description of their spectra. We also …
The paper studies non-integer curvature flows and proves convergence to spheres under specific conditions.
The study pinches the rigidity of self-shrinking surfaces in mean curvature flow.