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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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7 results for “bubble-sheet”

Classification of bubble-sheet ovals in

\mathbb{R}^{4}

math.DG

The paper classifies ovals in 4D space for a specific flow.

problem Classifying ovals in 4D space for a specific flow.

method Proving classification through symmetry and flow properties.

result Classified ovals in 4D space, up to scaling and rigid motion.

bubble-sheet ovals mean curvature flow 4D space symmetry ancient ovals

2022-09-11abs ↗pdf ↗

Hearing the shape of ancient noncollapsed flows in

\mathbb{R}^{4}

math.DG

Study ancient flows in 4D, classifying based on bubble-sheet eigenvalues.

problem Classify ancient noncollapsed flows in

\mathbb{R}^4

method Fine spectral analysis of bubble-sheet function

u

result Ancient flows in

\mathbb{R}^4

classified into three cases based on

Q

rank.

ancient flows mean curvature flows spectral analysis bubble-sheet spectral asymptotics

2021-07-09abs ↗pdf ↗

Precise asymptotics near a generic

\mathbb S^1\times\mathbb R^3

singularity of mean curvature flowmath.DG

In the present paper we study a type of generic singularity of mean curvature flow modelled on the bubble-sheet $\mathbb S^1\times\mathbb R^3$ , and we derive an asymptotic profile for a neighborhood of singularity.

2019-04-08abs ↗pdf ↗

A nonexistence result for wing-like mean curvature flows in

\mathbb{R}^4

math.DG

Paper disproves potential singularity models for 3D hypersurfaces in R^4.

problem Noncollapsed wing-like flows as singularity models for mean curvature flow in R^4.

method Fine bubble-sheet analysis generalizing fine neck analysis.

result Ancient noncollapsed flows in R^4 are always simple geometric shapes, not wedges.

mean curvature flow ancient flows singularity models R^4 fine neck analysis

2021-05-27abs ↗pdf ↗

κ

-solutions and canonical neighborhoods in 4d Ricci flowmath.DG

New 1-parameter family of ovals identified in 4d Ricci flow classification.

problem Classifying

κ

-solutions in 4d Ricci flow.

method Introducing conjectures and constructing new examples.

result Established canonical neighborhood theorem for 4d Ricci flow.

4d Ricci flow κ-solutions canonical neighborhoods ancient flows cylindrical singularities

2023-08-02abs ↗pdf ↗

Spectral quantization for ancient asymptotically cylindrical flowsmath.DG

The study quantizes ancient flows in cylinders, revealing their asymptotic behavior.

problem Analyzing ancient mean curvature flows with cylindrical tangent profiles.

method Proved asymptotic behavior of cylindrical profile functions using spectral quantization.

result Asymptotic behavior of cylindrical profile functions quantized to eigenvalues 0 or -sqrt(2(n-k))/4.

ancient flows cylindrical tangent spectral quantization asymptotic behavior mean curvature flows

2022-11-04abs ↗pdf ↗

Classification of ancient noncollapsed flows in

\mathbb{R}^4

math.DG

Classifies ancient noncollapsed flows in 4D space.

problem Classify all noncollapsed singularities of the mean curvature flow in R^4.

method Proves differential neck theorem, introduces new ideas like switch and differential Merle-Zaag dynamics.

result Classifies all ancient noncollapsed solutions in R^4.

mean curvature flow ancient solutions differential neck theorem ancient ovals self-similar translators

2024-12-13abs ↗pdf ↗