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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.

168,695 papers · 148 categories

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8 results for “hypertori”

Minimal hypertori in the four-dimensional spheremath.DG

Minimal hypertori found in 4D sphere, solving Bernstein conjecture.

problem Finding minimal embedded hypertori in 4D sphere.

method Analyzing minimally embedded and immersed hypertori and hyperspheres.

result Infinitely many non-isometric minimally embedded hypertori and hyperspheres found.

Minimal hypertori 4D sphere Bernstein conjecture Chern

2021-09-24abs ↗pdf ↗

Embedded constant mean curvature hypertori in the

2n

-spheremath.DG

Authors construct hypertori with constant negative mean curvature in a sphere.

problem Constructing constant mean curvature hypertori in a sphere.

method Constructing two different constant mean curvature

(2n-1)

-dimensional hypertori in a

2n

-dimensional sphere.

result Two different constant mean curvature

(2n-1)

-dimensional hypertori with negative mean curvature in a

2n

-dimensional sphere.

constant mean curvature hypertori sphere negative curvature

2025-03-25abs ↗pdf ↗

The stability index and Yau's conjecture for Carlotto-Schulz minimal hypertorimath.DG

The paper proves stability of minimal embeddings in spheres and relates it to Yau's conjecture.

problem Stability of minimal embeddings in spheres and Yau's conjecture.

method Analyzes stability index and solves differential equation to relate to Yau's conjecture.

result Stability index of minimal hypersurfaces is at least n^2+4n+3 and Yau's conjecture holds under specific conditions.

minimal embeddings stability index Yau's conjecture Carlotto-Schulz minimal hypertori differential equation

2025-08-12abs ↗pdf ↗

Smooth Normalizing Flowsstat.ML

Smooth flows for physical systems with smooth energies and forces.

problem Smooth energies for physical simulations and force computation.

method Smooth mixture transformations on compact intervals and hypertori, using root-finding and the inverse function theorem.

result Smooth flows allow training by force matching and use as molecular dynamics potentials.

normalizing flows smooth energies force matching molecular dynamics root-finding

2021-10-01abs ↗pdf ↗

Toral CW complexes and bifurcation control in Eulerian flows with multiple Hopf singularitiesmath.DS

Study controls bifurcations in Eulerian flows with multiple Hopf singularities.

problem Bifurcation analysis and control of nonlinear Eulerian flows with non-resonant n-tuple Hopf singularities.

method Analysis of CW complex bifurcations of flow-invariant Clifford hypertori, using leaf-bifurcation varieties.

result Tertiary toral CW complex bifurcates from and persists outside a secondary toral CW complex.

Eulerian flows Hopf singularities CW complexes bifurcation control Clifford hypertori

2020-02-21abs ↗pdf ↗

Minimal hypersurfaces in spheres generated by isoparametric foliationsmath.DG

Minimal hypersurfaces in spheres generated by isoparametric foliations are found.

problem Existence of minimal hypersurfaces in spheres generated by isoparametric foliations.

method Generalized rotational ansatz formed by the union of homothetic copies of isoparametric leaves, reducing the minimal surface equation to an ordinary differential equation.

result Closed embedded minimal hypersurfaces of topological type

S^1 imes M

are found for any isoparametric hypersurface

M \subset \mathbb{S}^n

Minimal hypersurfaces isoparametric foliations spheres topology ordinary differential equations

2026-03-04abs ↗pdf ↗

The stability index and Yau's conjecture for Carlotto-Schulz minimal hypertori, part IImath.DG

The paper refines the stability index for a specific minimal hypersurface and verifies Yau's conjecture.

problem Stability of minimal hypersurfaces in spheres and eigenvalue multiplicity.

method Analytical and numerical methods to study eigenvalues and stability indices.

result The multiplicity of the eigenvalue for the Carlotto-Schulz minimal embedding is at least 2n+1+n^2.

Minimal Hypersurfaces Eigenvalues Stability Operator Carlotto-Schulz Yau's Conjecture

2026-06-15abs ↗pdf ↗

Intrinsic Gaussian Vector Fields on Manifoldsstat.ML

The paper introduces novel Gaussian process models for vector-valued signals on manifolds.

problem Modeling vector-valued signals on non-Euclidean domains, especially for applications like wind speeds.

method Intrinsically defined Gaussian vector fields on manifolds, accounting for manifold geometry.

result Gaussian vector fields provide more refined inductive biases than extrinsic fields.

Gaussian process manifolds vector fields non-Euclidean domains wind speeds

2023-10-28abs ↗pdf ↗