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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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0111 · Jul 200619922001200920172026
4 results for “W-volume”
Epstein Surfaces, WW-Volume, and the Osgood-Stowe Differentialmath.DG

Develops new methods for Epstein surfaces and W-volume.

problem Constructing and understanding Epstein surfaces and W-volume.
method Alternate construction using Osgood-Stowe differential; variational formulas.
result Generalizations of Epstein's univalence criterion and variational formulas for W-volume.
Epstein surfacesW-volumeOsgood-Stowe differentialSchwarzian derivativeconvex co-compact hyperbolic 3-manifold
2024-02-23abs ↗pdf ↗
W-volume for planar domains with circular boundarymath.DG

Defines W-volume for planar domains with circular boundaries, relating to Laplacian determinant and Schottky uniformization.

problem Determining the volume of conformal metrics on planar domains with circular boundaries.
method Extending Epstein maps to conformal metrics, defining W-volume, using Schottky uniformization and Loewner energy.
result Shows a bound on the renormalized volume of Schottky uniformization and provides a realization of Loewner energy.
W-volumeconformal metricsSchottky uniformizationLoewner energyLaplacian determinant
2023-11-30abs ↗pdf ↗
A bound on the L2L^2-norm of a projective structure by the length of the bending laminationmath.GT

Bounds projective structure norms by bending lamination lengths.

problem Bounding the L2L^2-norm of projective structures.
method Using the Thurston parameterization and Krasnov-Schlenker's WW-volume theory.
result Upper bounds on L2L^2-norm of holomorphic quadratic differential by the length of bending lamination.
projective structurequadratic differentialbending laminationSchwarzian derivativeThurston parameterization
2022-01-21abs ↗pdf ↗
On the renormalized volume of hyperbolic 3-manifoldsmath.DG

The renormalized volume of hyperbolic manifolds is a quantity motivated by the AdS/CFT correspondence of string theory and computed via a certain regularization procedure. The main aim of the present paper is to elucidate its geometrical meaning. We use another regularization procedure based on surfaces equidistant to …

2006-07-04abs ↗pdf ↗