Results 51 to 60 of about 43,110 (140)
Random walk on sphere packings and Delaunay triangulations in arbitrary dimension
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We prove that random walks on a family of tilings of d$d$‐dimensional Euclidean space, with a canonical choice of conductances, converge to Brownian motion modulo time parameterization. This class of tilings includes Delaunay triangulations (the dual of Voronoi tessellations) and sphere packings.
Ahmed Bou‐Rabee, Ewain Gwynne
wiley +1 more source
Closed geodesics and the first Betti number
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We prove that, on any closed manifold of dimension at least two with non‐zero first Betti number, a C∞$C^\infty$ generic Riemannian metric has infinitely many closed geodesics, and indeed closed geodesics of arbitrarily large length. We derive this existence result combining a theorem of Mañé together with the following new theorem of ...
Gonzalo Contreras, Marco Mazzucchelli
wiley +1 more source
, 2018 A famous theorem of Weyl states that if $M$ is a compact submanifold of euclidean space, then the volumes of small tubes about $M$ are given by a polynomial in the radius $r$, with coefficients that are expressible as integrals of certain scalar ...
Fu, Joseph H. G., Wannerer, Thomas
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Asymptotics of quantum 6j$6j$‐symbols and generalized hyperbolic tetrahedra
Journal of Topology, Volume 18, Issue 3, September 2025.Abstract We establish the geometry behind the quantum 6j$6j$‐symbols under only the admissibility conditions as in the definition of the Turaev–Viro invariants of 3‐manifolds. As a classification, we show that the 6‐tuples in the quantum 6j$6j$‐symbols give in a precise way to the dihedral angles of (1) a spherical tetrahedron, (2) a generalized ...
Giulio Belletti, Tian Yang
wiley +1 more source
Legendrian non‐isotopic unit conormal bundles in high dimensions
Journal of Topology, Volume 18, Issue 3, September 2025.Abstract For any compact connected submanifold K$K$ of Rn$\mathbb {R}^n$, let ΛK$\Lambda _K$ denote its unit conormal bundle, which is a Legendrian submanifold of the unit cotangent bundle of Rn$\mathbb {R}^n$. In this paper, we give examples of pairs (K0,K1)$(K_0,K_1)$ of compact connected submanifolds of Rn$\mathbb {R}^n$ such that ΛK0$\Lambda _{K_0}$
Yukihiro Okamoto
wiley +1 more source
On positive scalar curvature and moduli of curves
, 2018 In this article we first show that any finite cover of the moduli space of closed Riemann surfaces of genus $g$ with $g\geq 2$ does not admit any Riemannian metric $ds^2$ of nonnegative scalar curvature such that $ds^2 \succ ds_{T}^2$ where $ds_{T}^2$ is
Liu, Kefeng, Wu, Yunhui
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On Isosystolic Inequalities for T^n, RP^n, and M^3
, 2013 If a closed smooth n-manifold M admits a finite cover whose Z/2Z-cohomology has the maximal cup-length, then for any riemannian metric g on M, we show that the systole Sys(M,g) and the volume Vol(M,g) of the riemannian manifold (M,g) are related by the ...
Nakamura, Kei
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A fundamental theorem for submanifolds in semi-Riemannian warped products [PDF]
Journal of Geometry and Physics, 2017 Carlos A. D. Ribeiro, Marcos F. de Melo
semanticscholar +1 more source
Slant Riemannian maps from almost Hermitian manifolds
, 2012 As a generalization of holomorphic submersions, anti-invariant submersions and slant submersions, we introduce slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds.
Sahin, Bayram
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