Toponogov's triangle comparison theorem in model spaces of nonconstant curvature

The Gauss - Bonnet - Grotemeyer Theorem in spaces of constant curvature ∗

In 1963, K.P. Grotemeyer proved an interesting variant of the Gauss-Bonnet Theorem. Let M be an oriented closed surface in the Euclidean space R 3 with Euler characteristic χ(M), Gauss curvature G and unit normal vector field n. Grote-meyer's identity replaces the Gauss-Bonnet integrand G by the normal moment (a · n) 2 G, where a is a fixed unit vector: M (a · n) 2 Gdv = 2π 3 χ(M). We generaliz...

Schauder Fixed Point Theorem in Spaces with Global Nonpositive Curvature

Path-integral Approach for Superintegrable Potentials on Spaces of Nonconstant Curvature: I. Darboux Spaces Di and Dii

In this paper the Feynman path-integral technique is applied for superintegrable potentials on two-dimensional spaces of nonconstant curvature: these spaces are Darboux spaces DI and DII, respectively. On DI there are three and on DII four such potentials, respectively. We are able to evaluate the path integral in the most of the separating coordinate systems, leading to expressions for the Gre...

Kirszbraun’s Theorem and Metric Spaces of Bounded Curvature

We generalize Kirszbraun’s extension theorem for Lipschitz maps between (subsets of) euclidean spaces to metric spaces with upper or lower curvature bounds in the sense of A.D. Alexandrov. As a byproduct we develop new tools in the theory of tangent cones of these spaces and obtain new characterization results which may be of independent interest.

comparison of catalytic activity of heteropoly compounds in the synthesis of bis(indolyl)alkanes.

heteropoly acids (hpa) and their salts have advantages as catalysts which make them both economically and environmentally attractive, strong br?nsted acidity, exhibiting fast reversible multi-electron redox transformations under rather mild conditions, very high solubility in polar solvents, fairly high thermal stability in the solid states, and efficient oxidizing ability, so that they are imp...