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.

168,742 papers · 148 categories

Trend · papers per month

count % of corpus

5 results for “r-convexity”

r

-convex set which is not locally contractiblemath.GT

Study finds a non-locally contractible $r$ -convex set.

problem Find an

r

-convex set which is not locally contractible.

method Constructs a counterexample of a non-locally contractible

r

-convex set.

result Proves that the class of supports with positive reach of absolutely continuous distributions includes strictly the class of

r

-convex supports.

r-convex set non-locally contractible counterexample shape restrictions set estimation

2022-11-15abs ↗pdf ↗

Computable bounds for the reach and

r

-convexity of subsets of

\mathbb{R}^d

math.ST

Computes bounds on reach and r-convexity from point cloud data.

problem Computing geometric properties of sets from sparse data.

method Computes upper bounds on reach and r-convexity from point cloud data.

result Bounds converge to true values as point cloud density increases.

convexity reach r-convexity point cloud geometric properties

2022-12-02abs ↗pdf ↗

On Large Scale Inductive Dimension of Asymptotic Resemblance Spacesmath.GT

We introduce the notion of large scale inductive dimension for asymptotic resemblance spaces. We prove that the large scale inductive dimension and the asymptotic dimensiongrad are equal in the class of r-convex metric spaces. This class contains the class of all geodesic metric spaces and all finitely generated groups…

2014-10-31abs ↗pdf ↗

Global geometry and

C^1

convex extensions of

1

-jetsmath.DG

Let $E$ be an arbitrary subset of $\mathbb{R}^n$ (not necessarily bounded), and $f:E\to\mathbb{R}$ , $G:E\to\mathbb{R}^n$ be functions. We provide necessary and sufficient conditions for the $1$ -jet $(f,G)$ to have an extension $(F, \nabla F)$ with $F:\mathbb{R}^n\to\mathbb{R}$ convex and of class $C^{1}$ . Besides, if $…

2017-06-29abs ↗pdf ↗

On compact embbeded Weingarten hypersurfaces in warped productsmath.DG

The study examines hypersurfaces in warped products and their properties.

problem Characterizing hypersurfaces in warped products satisfying a specific curvature condition.

method Analyzes hypersurfaces in warped products with a Weingarten condition and proves stability results.

result Hypersurfaces in space forms are geodesic spheres under certain curvature conditions.

Hypersurfaces Warped Products Weingarten Condition Stability Geodesic Spheres

2022-06-14abs ↗pdf ↗