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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.

168,742 papers · 148 categories

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6 results for “dilation-invariant”

Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measuresstat.ML

Topology-based information retrieval improves query accuracy.

problem Query accuracy in databases with complex structures.

method Dilation-invariant comparative measures of persistent homology.

result Topology-based retrieval outperforms standard methods.

topology persistent homology information retrieval dilation-invariant bottleneck distance

2021-04-04abs ↗pdf ↗

Entire spacelike radial graphs in the Minkowski space, asymptotic to the light-cone, with prescribed scalar curvaturemath.AP

Existence and uniqueness in ${\Bbb R}^{n,1}$ of entire spacelike hypersurfaces contained in the future of the origin $O$ and asymptotic to the light-cone, with scalar curvature prescribed at their generic point $M$ as a negative function of the unit vector $\overrightarrow{Om}$ pointing in the direction of $\overrighta…

2007-07-07abs ↗pdf ↗

High Codimension Curve Shortening Flow with Free Boundarymath.DG

Study curve shortening flow in high dimensions with boundary constraints.

problem Understanding the behavior of curves in high-dimensional spaces with boundary conditions.

method Used curvature and higher-derivative estimates, Stahl-type maximum principle, and blow-up analysis.

result Flow converges to a shrinking semicircle model or has only semicircle boundary singularities in low entropy regimes.

curve shortening flow high codimension free boundary Type I and II singularities shrinking semicircle model

2026-02-24abs ↗pdf ↗

Surfaces obtained from CP^(N-1) sigma modelsmath.DG

In this paper, the Weierstrass technique for harmonic maps S^2 -> CP^(N-1) is employed in order to obtain surfaces immersed in multidimensional Euclidean spaces. It is shown that if the CP^(N-1) model equations are defined on the sphere S^2 and the associated action functional of this model is finite, then the generali…

2008-02-08abs ↗pdf ↗

A rectifiability result for finite-perimeter sets in Carnot groupsmath.AP

New rectifiability criteria for finite-perimeter sets in Carnot groups.

problem Rectifiability of finite-perimeter sets in Carnot groups.

method Introducing a new notion of rectifiability based on cone properties and studying semigroups generated by horizontal half-spaces.

result Finite-perimeter subsets in Carnot groups can be covered by countably many subsets with cone properties, leading to countable rectifiability with respect to intrinsic Lipschitz graphs.

Carnot groups finite-perimeter sets rectifiability cone property semigroups

2019-12-01abs ↗pdf ↗

Classification of Minimal Immersions of Conformally Flat

3

-Tori and

4

-Tori in Spheres by The First Eigenfunctionsmath.DG

The paper classifies minimal immersions of flat 3- and 4-tori in spheres by their first eigenfunctions.

problem Classifying minimal immersions of flat 3- and 4-tori in spheres by their first eigenfunctions.

method General construction of homogeneous minimal flat n-tori in spheres, detailed investigations of shortest vectors in lattices.

result There exists a 2-parameter family of non-congruent λ1-minimal flat 4-tori.

minimal immersions flat tori spheres first eigenfunctions spectral geometry

2022-12-05abs ↗pdf ↗