Geometrical and topological aspects of Electrostatics on Riemannian manifolds
نویسندگان
چکیده
منابع مشابه
Geometrical versus Topological Properties of Manifolds
Given a compact n-dimensional immersed Riemannian manifold Mn in some Euclidean space we prove that if the Hausdorff dimension of the singular set of the Gauss map is small, then Mn is homeomorphic to the sphere Sn. Also, we define a concept of finite geometrical type and prove that finite geometrical type hypersurfaces with small set of points of zero GaussKronecker curvature are topologically...
متن کاملTopological Entropy and Blocking Cost for Geodesics in Riemannian Manifolds
For a pair of points x, y in a compact, riemannian manifold M let nt(x, y) (resp. st(x, y)) be the number of geodesic segments with length ≤ t joining these points (resp. the minimal number of point obstacles needed to block them). We study relationships between the growth rates of nt(x, y) and st(x, y) as t → ∞. We derive lower bounds on st(x, y) in terms of the topological entropy h(M) and it...
متن کاملA Geometry Preserving Kernel over Riemannian Manifolds
Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...
متن کاملFlowers on Riemannian manifolds
In this paper we will present two upper bounds for the length of a smallest “flower-shaped” geodesic net in terms of the volume and the diameter of a manifold. Minimal geodesic nets are critical points of the length functional on the space of graphs immersed into a Riemannian manifold. Let Mn be a closed Riemannian manifold of dimension n. We prove that there exists a minimal geodesic net that ...
متن کاملTopological aspects of geometrical signatures of phase transitions.
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical phi(4) models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the two-dimensional case, when a phase transition is present. The observed phenomenology strongly supports, though in an indirect way, a recently proposed topological conj...
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: Journal of Geometry and Physics
سال: 2007
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2007.02.003