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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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5 results for “half-volume”

The Half-Volume Spectrum of a Manifoldmath.DG

Defines half-volume spectrum for manifolds and proves Weyl law holds.

problem Understanding volume distribution in manifolds.

method Introduces half-volume spectrum and uses Weyl law and Allen-Cahn min-max theory.

result Weyl law holds for half-volume spectrum and half-volume constant achieved by specific surfaces.

manifolds volume spectrum Weyl law min-max theory half-volume

2023-02-15abs ↗pdf ↗

Equivalence of Almgren-Pitts and phase-transition half-volume spectramath.DG

Proves spectra equivalence for Riemannian manifolds.

problem Equivalence of Almgren-Pitts and phase-transition half-volume spectra.

method Proof of spectra equivalence for Riemannian manifolds.

result Confirms conjecture about spectra equivalence.

Riemannian manifolds spectra equivalence Almgren-Pitts phase-transition half-volume

2026-04-01abs ↗pdf ↗

Infinitely Many Half-Volume Constant Mean Curvature Hypersurfaces via Min-Max Theorymath.DG

The paper finds infinitely many half-volume CMC hypersurfaces on generic or Ricci-positive manifolds.

problem Finding infinitely many half-volume constant mean curvature (CMC) hypersurfaces on manifolds.

method Developed a min-max theory for non-local functionals to prove the existence of these hypersurfaces.

result Infinitely many geometrically distinct CMC hypersurfaces enclosing half the volume of a manifold.

CMC hypersurfaces min-max theory generic metrics Ricci-positive manifolds half-volume

2024-05-01abs ↗pdf ↗

Existence of singular isoperimetric regionsmath.DG

The paper finds singular isoperimetric regions in high-dimensional spaces.

problem Existence of singular isoperimetric regions in high-dimensional manifolds.

method Construction of specific manifolds with singular isoperimetric regions.

result Construction of manifolds with singular isoperimetric regions.

isoperimetric regions singularities high-dimensional manifolds Smale's construction

2023-02-14abs ↗pdf ↗

On the Isoperimetric Profile of the Hypercubemath.MG

The hypercube's perimeter is significantly larger than expected near half volume.

problem Understanding the isoperimetric profile of the hypercube.

method Analytical proof of perimeter bounds and comparison to Gaussian isoperimetric profile.

result The isoperimetric profile of the hypercube does not converge to the Gaussian profile as dimension increases.

hypercube isoperimetric profile perimeter dimensional convergence Brezis and Bruckstein conjecture

2023-05-31abs ↗pdf ↗