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.
Catenaries defined on any Riemannian surface using intrinsic distance.
problem Defining catenaries on Riemannian surfaces.
method Defining catenaries as critical points of a potential functional, calculating potential with intrinsic distance, and characterizing using curvature.
result Characterization of catenaries on various Riemannian surfaces.
The paper studies dual catenaries in the dual plane, deriving equations and characterizations.
problem Understanding catenaries in the dual plane.
method Introduced α-catenaries as stationary points of a potential energy functional, derived Euler-Lagrange equations, and geometrically characterized them.
result Explicit equations and geometric characterization of α-catenaries.
In this paper we generalize in Lorentz-Minkowski space ł3 the two-dimensional analogue of the catenary of Euclidean space. We solve the Dirichlet problem for bounded mean convex domains and spacelike boundary data that have a spacelike extension to the domain. We also classify all singular maximal surfaces of ł3 …
We consider an appoximation of a catenoid constructed from "odd" truncated cones that maintains minimality in a certain sense. Thorough this procedure, we obtain a discrete curve approximating a catenary by exploiting the fact that it is the function that generates a catenoid. In this investigation, the theory of the G…
In this paper, we consider the problem of finding the hypersurface M^n in the Euclidean (n+1)-space R^{n+1} that satisfies an equation of mean curvature type, called singular minimal hypersurface equation. Such an equation physically characterizes the hypersurfaces in the upper halfspace (R^{n+1})_{+} with lowest gravi…