On-device research index

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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3 results for “codimension-free”

L^p

-Sobolev inequalities on minimal submanifoldsmath.AP

The paper proves $L^p$ -Sobolev inequalities for minimal submanifolds.

problem Proving

L^p

-Sobolev inequalities for minimal submanifolds.

method Optimal mass transport theory on Euclidean submanifolds.

result Asymptotically sharp and codimension-free Sobolev constant for

p\geq 2

Sobolev inequalities minimal submanifolds optimal mass transport codimension-free asymptotically sharp

2024-12-11abs ↗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 ↗

Logarithmic-Sobolev inequalities on non-compact Euclidean submanifolds: sharpness and rigiditymath.DG

Sharp $L^p$ -logarithmic-Sobolev inequalities on submanifolds with applications to hypercontractivity.

problem Developing inequalities on submanifolds of Euclidean space.

method Optimal mass transport theory on submanifolds, sharpness analysis.

result Sharp inequalities and equality conditions for submanifolds.

logarithmic-Sobolev inequalities submanifolds sharpness rigidity hypercontractivity

2024-10-12abs ↗pdf ↗