Related papers: Geometric Integration by Parts and Sobolev Spaces …
We study completeness properties of reparametrization invariant Sobolev metrics of order $n\ge 2$ on the space of manifold valued open and closed immersed curves. In particular, for several important cases of metrics, we show that Sobolev…
The differential-geometric structure of the manifold of smooth shapes is applied to the theory of shape optimization problems. In particular, a Riemannian shape gradient with respect to the first Sobolev metric and the Steklov-Poincar\'{e}…
In this article we propose a definition of super Gromov-Witten invariants by postulating a torus localization property for the odd directions of the moduli spaces of super stable maps and super stable curves of genus zero. That is, we…
We classify globally generated vector bundles with first Chern class $c_1$ at least 4 on the projective 3-space with the property that $E(-c_1+3)$ has a non-zero global section. This (seemingly) technical result allows one to reduce the…
Finding constrained saddle points on Riemannian manifolds is significant for analyzing energy landscapes arising in physics and chemistry. Existing works have been limited to special manifolds that admit global regular level-set…
Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…
In this article, the authors introduce the Newton-Morrey-Sobolev space on a metric measure space $(\mathscr{X},d,\mu)$. The embedding of the Newton-Morrey-Sobolev space into the H\"older space is obtained if $\mathscr{X}$ supports a weak…
A form of Sobolev inequalities for the symmetric gradient of vector-valued functions is proposed, which allows for arbitrary ground domains in $\mathbb R ^n$. In the relevant inequalities, boundary regularity of domains is replaced with…
We study first-order Sobolev spaces on reflexive Banach spaces via relaxation, test plans, and divergence. We show the equivalence of the different approaches to the Sobolev spaces and to the related tangent bundles.
We introduce an extended Sobolev scale on a smooth compact manifold with boundary. The scale is formed by inner-product H\"ormander spaces for which an RO-varying radial function serves as a regularity index. These spaces do not depend on a…
We consider in this paper an area functional defined on submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric. Since the expression of this area depends on the degree, not all variations are…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
Sobolev spaces are a natural framework for the analysis of problems in partial differential equations and calculus of variations. Some physical and geometric contexts, such as liquid crystals models and harmonic maps, lead to consider…
The study presents a vector-valued extension of the classical Mercer theorem within the framework of reproducing kernel Hilbert spaces defined over Kaplansky-Hilbert modules associated with the algebra of essentially bounded measurable…
The paper presents some recent results on the Weil-Petersson geometry theory of the universal Teichm\"uller space, a topic which is important in Teichm\"uller theory and has wide applications to various areas such as mathematical physics,…
In 2005 Dullin et al. proved that the non-zero vector of Maslov indices is an eigenvector with eigenvalue 1 of the monodromy matrices of an integrable Hamiltonian system. We take a close look at the geometry behind this result and extend it…
Using Gutzmer's formula, due to Lassalle, we characterise the image of Sobolev spaces under the Segal-Bargmann transform on compact Riemannian symmetric spaces.
In this paper, combining the Rashevsky-Chow-Sussmann (orbit) theorem with the Ambrose-Singer theorem, we introduce the notion of controllable principal connections on principal $G$-bundles. Using this concept, under a mild assumption of…
It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddings of pseudo-Riemannian manifolds with symmetries into an…