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arXiv research

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.

168,657 papers · 148 categories

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← all fields·5 papers on “minimal hypersurfaces” in Differential Geometry · 1 month
Renormalized Area of Catenoids in the Hyperbolic Spacemath.DG

Study calculates the renormalized area of catenoids in hyperbolic spaces.

problem Calculating the renormalized area of catenoids in hyperbolic spaces.
method Variational characterization and Chern--Gauss--Bonnet formulas for locally conformally flat manifolds.
result Renormalized area of catenoids varies continuously from negative infinity to twice the area of totally geodesic hypersurfaces.
catenoidshyperbolic spacerenormalized areaminimal hypersurfacesvariational characterization
2026-07-13abs ↗pdf ↗
Topological Bernstein Theorems for Minimal Hypersurfaces in R4\R^4 confined in spacemath.DG

The study proves that certain minimal hypersurfaces in 4D space must be planes.

problem The extension of the half-space theorem to higher dimensions is obstructed.
method Analyzes topological properties of minimal hypersurfaces in R4\R^4.
result Complete, properly embedded minimal hypersurfaces in R4\R^4 with bounded curvature and diffeomorphic to R3\R^3 must be planes.
minimal hypersurfacestopological constraintsR^4catenoidhalf-space theorem
2026-07-07abs ↗pdf ↗
Topological Bernstein Theorems for Minimal Hypersurfaces in R4\mathbb{R}^4 confined in spacemath.DG

A 3D catenoid in 4D space is a minimal hypersurface that cannot be extended to a higher-dimensional half-space.

problem Extending the half-space theorem to higher dimensions in R4\mathbb{R}^4.
method Analyzing the topological constraints on minimal hypersurfaces in R4\mathbb{R}^4.
result A complete, properly embedded minimal hypersurface in a slab in R4\mathbb{R}^4 must be a hyperplane.
Minimal HypersurfacesTopological ConstraintsCatenoidHalf-Space TheoremVolume Growth
2026-07-07abs ↗pdf ↗