Related papers: Heterotopic energy for Sobolev mappings
We give a sharp lower bound for the energy in homotopy classes of mappings from real projective space to Riemannian manifolds, together with an upper bound for its infimum. We characterize the maps which attain this lower bound for energy,…
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…
We show that in all homotopy classes of mappings from complex projective space to Riemannian manifolds, the infimum of the energy is proportional to the infimal area in the homotopy class of mappings of the 2-sphere which represents the…
An approximation theorem of Youngs (1948) asserts that a continuous map between compact oriented topological 2-manifolds (surfaces) is monotone if and only if it is a uniform limit of homeomorphisms. Analogous approximation of Sobolev…
We study geometric variational problems for a class of effective models in quantum field theory known as Faddeev-Skyrme models. Mathematically one considers minimizing an energy functional on homotopy classes of maps from closed 3-manifolds…
We study the relationship between quasihomotopy and path homotopy for Sobolev maps between manifolds. We employ singular integrals on manifolds to show that, in the critical exponent case, path homotopy implies quasihomotopy - and observe…
The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled…
The energy of any $C^1$ representative of a homotopy class of maps from a compact and connected Riemannian manifold with nonnegative Ricci curvature into a complete Riemannian manifold with no conjugate points is bounded below by a constant…
Subtle issues arise when extending homotopy invariants to spaces of functions having little regularity, e.g., Sobolev spaces containing discontinuous functions. Sometimes it is not possible to extend the invariant at all, and sometimes,…
An energy for the homogeneous cosmological models is presented. More specifically, using an appropriate natural prescription, we find the energy within any region with any gravitational source for a large class of gravity theories--namely…
Let X and Y be planar Jordan domains of the same finite connectivity, Y being inner chordarc regular (such are Lipschitz domains). Every homeomorphism h:X->Y in the Sobolev space $W^{1,2}$ extends to a continuous map between closed domains.…
A free homotopy decomposition of any continuous map from a compact Riemmanian manifold $\mathcal{M}$ to a compact Riemannian manifold $\mathcal{N}$ into a finite number maps belonging to a finite set is constructed, in such a way that the…
We generalize the notion of calibrated submanifolds to smooth maps and show that the several examples of smooth maps appearing in the differential geometry become the examples of our situation. Moreover, we apply these notion to give the…
This paper contains two results on how homotopy limits of topological spaces interact with connectivity. The first is a formula for the connectivity of the homotopy limit of diagrams shaped over suitably finite categories, in terms of the…
Our goal is to clarify the relation between entanglement and correlation energy in a bipartite system with infinite dimensional Hilbert space. To this aim we consider the completely solvable Moshinsky's model of two linearly coupled…
The present paper is devoted to a theory of profile decomposition for bounded sequences in \emph{homogeneous} Sobolev spaces, and it enables us to analyze the lack of compactness of bounded sequences. For every bounded sequence in…
In this paper, we establish compactness for various geometric curvature energies including integral Menger curvature, and tangent-point repulsive potentials, defined a priori on the class of compact, embedded $m$-dimensional Lipschitz…
We study the Cauchy problem for the semilinear heat equation with the singular potential, called the Hardy-Sobolev parabolic equation, in the energy space. The aim of this paper is to determine a necessary and sufficient condition on…
We extend Siu's and Sampson's celebrated rigidity results to non-compact domains. More precisely, let $M$ be a smooth quasi-projective variety with universal cover $\tilde M$ and let $\tilde X$ be a symmetric space of non-compact type, a…
We construct homotopy formulas for the $\overline\partial$-equation on convex domains of finite type that have optimal Sobolev and H\"older estimates. For a bounded smooth finite type convex domain $\Omega\subset\mathbb C^n$ that has…