Results 101 to 110 of about 70,602 (222)

Regularity of solutions of the isoperimetric problem that are close to a smooth manifold

, 2017
In this work we consider a question in the calculus of variations motivated by riemannian geometry, the isoperimetric problem. We show that solutions to the isoperimetric problem, close in the flat norm to a smooth submanifold, are themselves smooth and $
Nardulli, Stefano
core   +1 more source

BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups

Analysis and Geometry in Metric Spaces, 2015
Let f : G → H be a Lipschitz map between two Carnot groups. We show that if B is a ball of G, then there exists a subset Z ⊂ B, whose image in H under f has small Hausdorff content, such that B\Z can be decomposed into a controlled number of pieces, the ...
Li Sean
doaj   +1 more source

A note on the magnetic Steklov operator on functions

Mathematika, Volume 71, Issue 4, October 2025.
Abstract We consider the magnetic Steklov eigenvalue problem on compact Riemannian manifolds with boundary for generic magnetic potentials and establish various results concerning the spectrum. We provide equivalent characterizations of magnetic Steklov operators which are unitarily equivalent to the classical Steklov operator and study bounds for the ...
Tirumala Chakradhar, Katie Gittins, Georges Habib, Norbert Peyerimhoff   +3 more
wiley   +1 more source

Left-invariant paracontact metric structure on a group Sol

Дифференциальная геометрия многообразий фигур
Among Thurston's famous list of eight three-dimensional geometries is the geometry of the manifold Sol. The variety Sol is a connected simply connected Lie group of real matrices of a special form.
M. V. Sorokina, O. P. Surina
doaj   +1 more source

Uniform Gaussian Bounds for Subelliptic Heat Kernels and an Application to the Total Variation Flow of Graphs over Carnot Groups

Analysis and Geometry in Metric Spaces, 2013
In this paper we study heat kernels associated with a Carnot group G, endowed with a family of collapsing left-invariant Riemannian metrics σε which converge in the Gromov- Hausdorff sense to a sub-Riemannian structure on G as ε→ 0.
Capogna Luca, Citti Giovanna, Manfredini Maria   +2 more
doaj   +1 more source

Geometric inequalities, stability results and Kendall's problem in spherical space

Mathematika, Volume 71, Issue 4, October 2025.
Abstract In Euclidean space, the asymptotic shape of large cells in various types of Poisson‐driven random tessellations has been the subject of a famous conjecture due to David Kendall. Since shape is a geometric concept and large cells are identified by means of geometric size functionals, the resolution of the conjecture is inevitably connected with
Daniel Hug, Andreas Reichenbacher
wiley   +1 more source

Nonexistence results of nonnegative solutions of elliptic equations and systems on the Heisenberg group

AIMS Mathematics
This paper establishes sharp nonexistence criteria for nonnegative solutions to a class of quasilinear elliptic inequalities and divergence-type systems in the subelliptic framework of the Heisenberg group $ H^n $.
Wei Shi
doaj   +1 more source

The porous medium equation: Large deviations and gradient flow with degenerate and unbounded diffusion

Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1609-1655, September 2025.
Abstract The problem of deriving a gradient flow structure for the porous medium equation which is thermodynamic, in that it arises from the large deviations of some microscopic particle system is studied. To this end, a rescaled zero‐range process with jump rate g(k)=kα,α>1$g(k)=k^\alpha, \alpha >1$ is considered, and its hydrodynamic limit and ...
Benjamin Gess, Daniel Heydecker
wiley   +1 more source

Connections in sub-Riemannian geometry of parallelizable distributions [PDF]

International Journal of Geometric Methods in Modern Physics, 2017
The notion of a parallelizable distribution has been introduced and investigated. A non-integrable parallelizable distribution carries a natural sub-Riemannian structure. The geometry of this structure has been studied from the bi-viewpoint of absolute parallelism geometry and sub-Riemannian geometry.
Ebtsam H. Taha, Nabil L. Youssef
openaire   +3 more sources

On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation

Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1783-1842, September 2025.
Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
wiley   +1 more source