Results 31 to 40 of about 529 (81)

Inverse mean curvature flow in quaternionic hyperbolic space

, 2017
In this paper we complete the study started in [Pi2] of evolution by inverse mean curvature flow of star-shaped hypersurface in non-compact rank one symmetric spaces.
Brown, André EX, Ch'ng, Quee-Lim, Currie, Michael, Grundy, Laura J, Hokanson, Jim, Javer, Avelino, Kerr, Rex, Lee, Chee Wai, Li, Chris, Li, Kezhi, Schafer, William R, Yemini, Eviatar   +11 more
core   +10 more sources

Curvature exponent and geodesic dimension on Sard-regular Carnot groups

Analysis and Geometry in Metric Spaces
In this study, we characterize the geodesic dimension NGEO{N}_{{\rm{GEO}}} and give a new lower bound to the curvature exponent NCE{N}_{{\rm{CE}}} on Sard-regular Carnot groups.
Golo Sebastiano Nicolussi, Zhang Ye
doaj   +1 more source

Rigidity of fiber-preserving quasisymmetric maps

, 2015
We show that fiber-preserving quasisymmetric maps are biLipschitz. As an application, we show that quasisymmetric maps on Carnot groups with reducible first stratum are ...
Donne, Enrico Le, Xie, Xiangdong
core   +1 more source

Invertible Carnot Groups [PDF]

, 2016
We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the $J^2$-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity.
Freeman, David M.
core  

A note on the diameter of small sub-Riemannian balls

Analysis and Geometry in Metric Spaces
We observe that the diameter of small (in a locally uniform sense) balls in C 1,1 sub-Riemannian manifolds equals twice the radius. We also prove that, when the regularity of the structure is further lowered to C 0, the diameter is arbitrarily close to ...
Di Marco Marco, Somma Gianluca, Vittone Davide   +2 more
doaj   +1 more source

On an evolution equation in sub-Finsler geometry

Analysis and Geometry in Metric Spaces
We study the gradient flow of an energy with mixed homogeneity, which is at the interface of Finsler and sub-Riemannian geometry.
Garofalo Nicola
doaj   +1 more source

Hopf fibration: geodesics and distances

, 2010
Here we study geodesics connecting two given points on odd-dimensional spheres respecting the Hopf fibration. This geodesic boundary value problem is completely solved in the case of 3-dimensional sphere and some partial results are obtained in the ...
Agrachev, Alexander Vasil’ev, Anastopoulos, Bauer, Berry, Boscain, Boscain, Bouwmeester, Calin, Calin, Chang, Chow, Der-Chen Chang, Hurtado, Irina Markina, Milnor, Montgomery, Mosseri, Pancharatnam, Radtke, Rashevskiĭ, Strichartz, Strichartz, Urbantke, Urbantke   +24 more
core   +1 more source

On the role of embeddability in conformal pseudo-hermitian geometry

Analysis and Geometry in Metric Spaces
In this article, we review some recent results about the role of embeddability in conformal CR (Cauchy-Riemann) geometry. We will show how this condition enters in the second variation of the pseudo-hermitian counterpart of the Einstein-Hilbert action ...
Malchiodi Andrea
doaj   +1 more source

Partial Isometries of a Sub-Riemannian Manifold

, 2012
In this paper, we obtain the following generalisation of isometric $C^1$-immersion theorem of Nash and Kuiper. Let $M$ be a smooth manifold of dimension $m$ and $H$ a rank $k$ subbundle of the tangent bundle $TM$ with a Riemannian metric $g_H$.
Eliashberg Y., Kuiper N. H., MAHUYA DATTA, Spring D.   +3 more
core   +1 more source

Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates

Advanced Nonlinear Studies
On general Carnot groups, the definition of a possible hypoelliptic Hodge-Laplacian on forms using the Rumin complex has been considered in (M. Rumin, “Differential geometry on C-C spaces and application to the Novikov-Shubin numbers of nilpotent Lie ...
Baldi Annalisa, Tripaldi Francesca
doaj   +1 more source