Anisotropic quaternion Carnot groups: Geometric analysis and Green function
نویسندگان
چکیده
منابع مشابه
A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices
The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...
متن کاملIsodiametric Inequality in Carnot Groups
The classical isodiametric inequality in the Euclidean space says that balls maximize the volume among all sets with a given diameter. We consider in this paper the case of Carnot groups. We prove that for any Carnot group equipped with a Haar measure one can find a homogeneous distance for which this fails to hold. We also consider Carnot-Carathéodory distances and prove that this also fails f...
متن کاملChaotic Geodesics in Carnot Groups
Graded nilpotent Lie groups, or Carnot Groups are to subRiemannian geometry as Euclidean spaces are to Riemannian geometry. They are the metric tangent cones for this geometry. Hoping that the analogy between subRiemannian and Riemannian geometry is a strong one, one might conjecture that the subRiemannian geodesic flow on any Carnot group is completely integrable. We prove this conjecture is f...
متن کاملConvex Functions on Carnot Groups
We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions of homogeneous elliptic equations.
متن کاملThe rigidity problem for Carnot groups
The observations in this talk come from a paper in preparation by A. Čap, M. Cowling, F. De Mari, M. Eastwood and R. McCallum about the Heisenberg group and the flag manifold, and more general papers by Cowling, De Mari, A. Korányi and H.M. Reimann, one published [?] and one in preparation, as well as papers by McCallum (in preparation) and B. Warhurst [?]. A Carnot group N is a connected, simp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2007
ISSN: 0196-8858
DOI: 10.1016/j.aam.2007.02.002