This paper extends parts of the results from [14] for plane curves to the case of surfaces in Rn. Let M be a compact connected oriented manifold of dimension less than n without boundary. Then shape space is either the manifold of submanifolds of Rn of type M , or the orbifold of immersions from M to Rn modulo the group of diffeomorphisms of M . We investigate the Sobolev Riemannian metrics on ...

We prove that in a convex metric space (X, d), an existence set K having a lower semi continuous metric projection is a δ-sun and in a complete M -space, a Chebyshev set K with a continuous metric projection is a γ-sun as well as almost convex.

1 Overview 1. This talk is about geodesics in the infinite dimensional symmetric space of Kähler metrics in a fixed Kähler classá la Donaldson-Semmes. 2. These geodesics are solutions of a homogeneous complex Monge-Ampère equation in 'space-time'. One would like to know existence, regularity... 3. Phong-Sturm proved that one can construct weak solutions by special polynomial approximations. The...

This paper extends parts of the results from [10] for plane curves to the case of hypersurfaces in R. Let M be a compact connected oriented n − 1 dimensional manifold without boundary. Then shape space is either the manifold of submanifolds of R of type M , or the orbifold of immersions from M to R modulo the group of diffeomorphisms of M . We investigate the Sobolev Riemannian metrics on shape...

Abstract. Let (X, d, μ) be a metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions, which is called nonhomogeneous metric measure space. In this paper, via a sharp maximal operator, the boundedness of commutators generated by multilinear singular integral with RBMO(μ) function on non-homogeneous metric measure spaces in m-multiple Lebesgue spa...

in this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in cat(0) spaces as well as in uced banach spaces. moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...

and Applied Analysis 3 effectively larger than that of the ordinary conemetric spaces. That is, every cone metric space is a cone b-metric space, but the converse need not be true. The following examples show the above remarks. Example 7. Let X = {−1, 0, 1}, E = R, andP = {(x, y) : x ≥ 0, y ≥ 0}. Define d : X × X → P by d(x, y) = d(y, x) for all x, y ∈ X, d(x, x) = θ, x ∈ X, and d(−1, 0) = (3, ...

considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. this paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong hausdorff topology.we study interrelationships between this theory and other fuzzy theories suchas intuitionis...