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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.

168,695 papers · 148 categories

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3 results for “f-neighbors”

Hopf-type Theorems For

f

-neighborsmath.MG

Study of $f$ -neighbors in Riemannian manifolds, proving infinite set of distances.

problem Exploring variations of Hopf theorem in Riemannian manifolds.

method Investigates continuous maps of compact Riemannian manifolds to

\mathbb{R}^m

and introduces

f

-neighbors.

result Set of distances realized as visual

f

-neighbors is infinite.

Riemannian manifolds continuous maps f-neighbors visual $f$-neighbors infinite set of distances

2022-08-29abs ↗pdf ↗

Hopf-type theorems for convex surfacesmath.MG

The paper extends Hopf's theorem to convex surfaces and discrete triangulations.

problem Extending Hopf's theorem to convex surfaces and discrete triangulations.

method Investigates continuous maps and simplicial maps on convex polyhedra, proving theorems about neighbors and distances.

result The Hopf theorem and its quantitative generalization hold for convex surfaces, with quasigeodesics replacing geodesics.

Hopf theorem convex surfaces Alexandrov geometry discrete maps triangulations

2025-04-20abs ↗pdf ↗

Borsuk-Ulam Type Theorems and Mountain Climbing Problemmath.AT

New theorem connects distant points and identical points on manifolds.

problem Continuous maps and distant points on manifolds.

method Qualitative extension of Hopf theorem, using topological 'distant' points.

result Existence of connected component containing both distant and identical points.

Borsuk-Ulam theorem Mountain climbing lemma Continuous maps Distant points Triangulable manifolds

2026-04-06abs ↗pdf ↗