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.
Sharp inequality found on three-balls for fourth order Sobolev traces.
We prove that the space of smooth Riemannian metrics on the three-ball with non-negative Ricci curvature and strictly convex boundary is path connected; and, moreover, that the associated moduli space (i.e., modulo orientation-preserving diffeomorphisms of the three-ball) is contractible. As an application, using resul…
New findings on Helmholtz equation solutions show exponential growth in constant for three ball inequality.
In the Euclidean unit three-ball, we construct compact, embedded, two-sided free boundary minimal surfaces with connected boundary and prescribed high genus, by a gluing construction tripling the equatorial disc. Aside from the equatorial disc itself, these are the first examples in the three-ball of compact free bound…
The study proves the existence of free boundary minimal disks in convex regions.
We give an algorithm for a surgery description of a -fold cyclic branched cover of branched along a tangle. We generalize constructions of Montesinos and Akbulut-Kirby.
Constructs minimal surfaces near the boundary of a ball.
Proves uniqueness of catenoid-like shapes in a ball.
We show that, among free boundary minimal surfaces in the unit ball in the three-dimensional Euclidean space, the flat equatorial disk and the critical catenoid are characterised by a pinching condition on the length of their second fundamental form.
Study finds conditions for free boundary CMC surfaces in conformally Euclidean 3-balls.
No free boundary Möbius bands exist in a 3D ball.
The study classifies surfaces with specific curvature properties.
In this note we revisit the notion of conformal barycenter of a measure on $\SS^n$ as defined by Douady and Earle in Acta Math. Vol 157, 1986. The aim is to extend rational maps from the Riemann sphere $\Cbar\isom\SS^2$ to the (hyperbolic) three ball $\BB^3$ and thus to $\SS^3$ by reflection. The construction which was…
We construct a new family of high genus examples of free boundary minimal surfaces in the Euclidean unit 3-ball by desingularizing the intersection of a coaxial pair of a critical catenoid and an equatorial disk. The surfaces are constructed by singular perturbation methods and have three boundary components. They are …
Active inference selects actions to maximize information gain, aiding structure learning.