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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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6 results for “p-elasticae”

Stability of flat-core pinned p-elasticaemath.AP

Classifies stability of flat-core $p$ -elasticae pinned at boundaries.

problem Stability of flat-core

p

-elasticae under pinned boundary conditions.

method Classification based on previous work for all

p\in(1,\infty)

and

d\geq2

result Completes the classification of stable pinned

p

-elasticae in

\mathbf{R}^d

stability p-elasticae flat-core pinned boundary classification

2025-08-14abs ↗pdf ↗

Complete classification of planar p-elasticaemath.AP

This paper classifies all planar p-elasticae and their properties.

problem Understanding the properties of p-elasticae in the plane.

method Introducing new types of p-elliptic functions to classify all planar p-elasticae.

result Explicit formulae and optimal regularity of all planar p-elasticae are obtained.

p-elasticae plane geometry p-elliptic functions critical points total squared curvature

2022-03-16abs ↗pdf ↗

Regularity and structure of non-planar

p

-elasticaemath.AP

Analytic non-planar $p$ -elasticae are shown to be 3D.

problem Classifying non-planar

p

-elasticae.

method Analyticity and structure results for

p

-elasticae in

\mathbb{R}^n

result Every non-planar

p

-elastica is analytic and three-dimensional.

p-elasticae analyticity structure non-planar Li-Yau inequality

2025-01-14abs ↗pdf ↗

Pinned planar p-elasticaemath.DG

Classifies pinned $p$ -elasticae and finds unique optimality exponents.

problem Classifying and understanding

p

-elasticae under pinned boundary conditions.

method Classification and analysis of

p

-elasticae, proving uniqueness and existence.

result Discovery of a unique exponent

p \simeq 1.5728

for full optimality.

p-elasticae p-bending energy minimizers Li-Yau inequality p-elastic networks

2022-09-13abs ↗pdf ↗

Variational stabilization of degenerate p-elasticaemath.AP

New stabilization found in planar elasticae with degenerate diffusion.

problem Existence of local minimizers in degenerate

p

-elasticae.

method Analysis of pinned planar

p

-elasticae with degenerate diffusion.

result Uncountably many local minimizers with diverging energy in degenerate regime.

p-elasticae degenerate diffusion local minimizers stabilization

2023-10-11abs ↗pdf ↗

General rigidity principles for stable and minimal elastic curvesmath.DG

Unified approach classifies stable and minimal elastic curves.

problem Classifying stable and minimal elastic curves under various conditions.

method Unified geometric approach using a `cut-and-paste` trick.

result Complete classification of stable closed

p

-elasticae and stable pinned

p

-elasticae.

rigidity principles elastic curves curvature energy global minimizers local minimizers

2023-01-20abs ↗pdf ↗