Results 51 to 60 of about 732 (169)

Constant curvature models in sub-Riemannian geometry

Journal of Geometry and Physics, 2019
The second version reflected comments from the reviewing process. Introduction and parts of exposition are extended, some proofs made more precise.
Alekseevsky, D., Medvedev, A., Slovak, J.   +2 more
openaire   +3 more sources

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

Predicting Crack Propagation in Brittle TPMS Under Uniaxial Loading: A Dual Concept Approach via Geodesic Lines and Cross‐Sectional Analysis

International Journal of Ceramic Engineering &Science, Volume 8, Issue 4, July 2026.
Cracking in brittle TPMS structures is governed by their geometry, with cracks propagating along geodesic paths determined by the initial crack orientation. Regions with small cross‐sections and abrupt area transitions identify critical damage regions and explain the differences in compressive strength among Primitive, Gyroid, Neovius, and IWP designs.
Thi Ngoc Diep Tran, Vinit Vijay Deshpande, Romana Piat   +2 more
wiley   +1 more source

Corrections to: ``Sub-Riemannian geometry''

Journal of Differential Geometry, 1989
An error in the proof of Corollary 6.2 of [1] has been pointed out by Gerard Ben-Arous. The computation of M(x,λ) in the case λo = 0 on p. 243 is incorrect, because M(x,λ) = 0 when λ0 = 0 and λjg (x) = 0 for all k. (There is also a factor of \ missing in the formula as stated for λ0 φ 0, but this is not significant.) Thus when applying the Pontryagin ...
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Subgraph entropy

Bulletin of the London Mathematical Society, Volume 58, Issue 6, June 2026.
Abstract Given r⩾3$r \geqslant 3$, we prove that there exists λ>0$\lambda >0$ depending only on r$r$ so that if G$G$ is a metric graph of rank r$r$ with metric entropy 1, then there exists a proper subgraph H$H$ of G$G$ with metric entropy at least λ$\lambda$. This answers a question of the second two authors together with Rieck. We interpret this as a
Tawfiq Hamed, Tarik Aougab, Matt Clay
wiley   +1 more source

On the tightness of left‐invariant contact structures

Bulletin of the London Mathematical Society, Volume 58, Issue 6, June 2026.
Abstract We prove that all left‐invariant contact structures on three‐dimensional Lie groups are tight. The argument is based on Riemannian methods and establishes a unique factorization property for any Lie group admitting a left‐invariant contact structure, other than SU(2)$\mathrm{SU}(2)$. We then make use of such factorization property to construct
Eugenio Bellini
wiley   +1 more source

A connection theoretic approach to sub-Riemannian geometry [PDF]

Journal of Geometry and Physics, 2003
We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism. In particular, some necessary and sufficient conditions for the existence of abnormal extremals will be derived.
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Cohomogeneity‐one solitons in Laplacian flow: Local, smoothly‐closing and steady solitons

Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.
Abstract We initiate a systematic study of cohomogeneity‐one solitons in Bryant's Laplacian flow of closed G2$\text{G}_2$‐structures on a 7‐manifold, motivated by the problem of understanding finite‐time singularities of that flow. Here, we focus on solitons with symmetry groups Sp(2)${\rm Sp}(2)$ and SU(3)${\rm SU}(3)$; in both cases, we prove the ...
Mark Haskins, Johannes Nordström
wiley   +1 more source

Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry

Journal de l’École polytechnique — Mathématiques, 2023
We use techniques from nonsmooth analysis and geometric measure theory to provide new examples of complete sub-Riemannian structures satisfying the Minimizing Sard conjecture. In particular, we show that complete sub-Riemannian structures associated with distributions of co-rank 2
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Topics in sub-Riemannian geometry

Russian Mathematical Surveys, 2016
This thesis is concerned with three different problems in sub-Riemannian geometry faced during my PhD. The first one is a problem in differential geometry and is about the local conformal classification of a certain class of sub-Riemannian structures. In the second one we deal with topology, and our main result establish some path-fibration properties ...
openaire   +4 more sources