Results 71 to 80 of about 228,756 (169)

Mori geometry meets Cartan geometry: Varieties of minimal rational tangents [PDF]

arXiv, 2015
We give an introduction to the theory of varieties of minimal rational tangents, emphasizing its aspect as a fusion of algebraic geometry and differential geometry, more specifically, a fusion of Mori geometry of minimal rational curves and Cartan geometry of cone structures.
arxiv  

Sub-Riemannian Geometry of Curves and Surfaces in Roto-Translation Group Associated with Canonical Connection

Mathematics
The aim of this paper is to obtain the sub-Riemannian properties of the roto-translation group RT. At the same time, we compute the sub-Riemannian limits of Gaussian curvature associated with two kinds of canonical connections for a C2-smooth surface in ...
Han Zhang, Haiming Liu
doaj   +1 more source

Calderón–Zygmund theory on some Lie groups of exponential growth

Mathematische Nachrichten, Volume 298, Issue 1, Page 113-141, January 2025.
Abstract Let G=N⋊A$G = N \rtimes A$, where N$N$ is a stratified Lie group and A=R+$A= \mathbb {R}_+$ acts on N$N$ via automorphic dilations. We prove that the group G$G$ has the Calderón–Zygmund property, in the sense of Hebisch and Steger, with respect to a family of flow measures and metrics.
Filippo De Mari, Matteo Levi, Matteo Monti, Maria Vallarino   +3 more
wiley   +1 more source

General Geometry and Geometry of Electromagnetism [PDF]

arXiv, 2002
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism.
arxiv  

Metric SYZ conjecture and non-archimedean geometry [PDF]

arXiv, 2020
We show that assuming a conjecture in non-archimedean geometry, then a metric formulation of the SYZ conjecture can be proved in large generality.
arxiv  

Sub-Riemannian geometry and Lie groups. Part II. Curvature of metric spaces, coadjoint orbits and associated representations

, 2004
This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups.
Buliga, Marius
core   +1 more source

Invariants, volumes and heat kernels in sub-Riemannian geometry [PDF]

, 2011
Sub-Riemannian geometry can be seen as a generalization of Riemannian geometry under non-holonomic constraints. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators (see [32, 57, 70 ...
Barilari, Davide
core  

Convex Hull Property and Exclosure Theorems for H-Minimal Hypersurfaces in Carnot Groups

Analysis and Geometry in Metric Spaces, 2016
In this paper, we generalize to sub-Riemannian Carnot groups some classical results in the theory of minimal submanifolds. Our main results are for step 2 Carnot groups.
Montefalcone Francescopaolo
doaj   +1 more source

Embedded trace operator for infinite metric trees

Mathematische Nachrichten, Volume 298, Issue 1, Page 190-243, January 2025.
Abstract We consider a class of infinite weighted metric trees obtained as perturbations of self‐similar regular trees. Possible definitions of the boundary traces of functions in the Sobolev space on such a structure are discussed by using identifications of the tree boundary with a surface.
Valentina Franceschi, Kiyan Naderi, Konstantin Pankrashkin   +2 more
wiley   +1 more source

Differential-geometric characterizations of complete intersections [PDF]

arXiv, 1994
The exposition has been significantly altered, hopefully improved.
arxiv