Search results for "Mathematica"
showing 10 items of 7971 documents
Feuilletages Riemanniens singuliers
2006
Abstract We prove that a singular foliation on a compact manifold admitting an adapted Riemannian metric for which all leaves are minimal must be regular. To cite this article: V. Miquel, R.A. Wolak, C. R. Acad. Sci. Paris, Ser. I 342 (2006).
The structure of Fedosov supermanifolds
2009
Abstract Given a supermanifold ( M , A ) which carries a supersymplectic form ω , we study the Fedosov structures that can be defined on it, through a set of tensor fields associated to any symplectic connection ∇ . We give explicit recursive expressions for the resulting curvature and study the particular case of a base manifold M with constant holomorphic sectional curvature.
Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces
2003
Abstract We use the heat equation to establish the Lipschitz continuity of Cheeger-harmonic functions in certain metric spaces. The metric spaces under consideration are those that are endowed with a doubling measure supporting a (1,2)-Poincare inequality and in addition supporting a corresponding Sobolev–Poincare-type inequality for the modification of the measure obtained via the heat kernel. Examples are given to illustrate the necessity of our assumptions on these spaces. We also provide an example to show that in the general setting the best possible regularity for the Cheeger-harmonic functions is Lipschitz continuity.
Hasse diagrams and orbit class spaces
2011
Abstract Let X be a topological space and G be a group of homeomorphisms of X. Let G ˜ be an equivalence relation on X defined by x G ˜ y if the closure of the G-orbit of x is equal to the closure of the G-orbit of y. The quotient space X / G ˜ is called the orbit class space and is endowed with the natural order inherited from the inclusion order of the closure of the classes, so that, if such a space is finite, one can associate with it a Hasse diagram. We show that the converse is also true: any finite Hasse diagram can be realized as the Hasse diagram of an orbit class space built from a dynamical system ( X , G ) where X is a compact space and G is a finitely generated group of homeomo…
Supermanifolds, Symplectic Geometry and Curvature
2016
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.
Strongly measurable Kurzweil-Henstock type integrable functions and series
2008
We give necessary and sufficient conditions for the scalar Kurzweil-Henstock integrability and the Kurzweil-Henstock-Pettis integrability of functions $f:[1, infty) ightarrow X$ defined as $f=sum_{n=1}^infty x_n chi_{[n,n+1)}$. Also the variational Henstock integrability is considered
Sharp estimate on the inner distance in planar domains
2020
We show that the inner distance inside a bounded planar domain is at most the one-dimensional Hausdorff measure of the boundary of the domain. We prove this sharp result by establishing an improved Painlev\'e length estimate for connected sets and by using the metric removability of totally disconnected sets, proven by Kalmykov, Kovalev, and Rajala. We also give a totally disconnected example showing that for general sets the Painlev\'e length bound $\kappa(E) \le\pi \mathcal{H}^1(E)$ is sharp.
Quasisymmetric Koebe uniformization with weak metric doubling measures
2020
We give a characterization of metric spaces quasisymmetrically equivalent to a finitely connected circle domain. This result generalizes the uniformization of Ahlfors 2-regular spaces by Merenkov and Wildrick. peerReviewed
Dirichlet approximation and universal Dirichlet series
2016
We characterize the uniform limits of Dirichlet polynomials on a right half plane. In the Dirichlet setting, we find approximation results, with respect to the Euclidean distance and {to} the chordal one as well, analogous to classical results of Runge, Mergelyan and Vitushkin. We also strengthen the notion of universal Dirichlet series.