Related papers: A Compact Embedding Theorem for Generalized Sobole…

We solve the classical problem of Plateau in every metric space which is $1$-complemented in an ultra-completion of itself. This includes all proper metric spaces as well as many locally non-compact metric spaces, in particular, all dual…

In the present paper, we deal with a new continuous and compact embedding theorems for the fractional Orlicz-Sobolev spaces, also, we study the existence of infinitely many nontrivial solutions for a class of non-local fractional…

We give sufficient geometric conditions, not involving capacities, for a compact null set to be removable for the Sobolev functions on weighted $\mathbb R^n$, defined as the closure of smooth functions in the weighted Sobolev norm. Our…

We study a modified version of Lerman-Whitehouse Menger-like curvature defined for m+2 points in an n-dimensional Euclidean space. For 1 <= l <= m+2 and an m-dimensional subset S of R^n we also introduce global versions of this discrete…

We prove that any metric of non-positive curvature in the sense of Alexandrov on a compact surface can be isometrically embedded as a convex spacelike Cauchy surface in a flat spacetime of dimension (2+1). The proof follows from polyhedral…

This study aims to investigate the functional properties of weak solution spaces and their compact embedding properties in relation to the Dirichlet problem associated with a specific class of degenerate elliptic equations. To expand the…

In previous work, the authors established a generalized version of Schmidt's subspace theorem for closed subschemes in general position in terms of Seshadri constants. We extend our theorem to weighted sums involving closed subschemes in…

Defect of compactness for non-compact imbeddings of Banach spaces can be expressed in the form of a profile decomposition. This paper extends the profile decomposition for Sobolev spaces proved by Solimini (AIHP 1995) to the non-reflexive…

In this paper we prove the Sobolev embeddings for Herz-type Triebel-Lizorkin spaces, \begin{equation*} \dot{K}_{q}^{\alpha_{2},r}F_{\theta }^{s_{2}}\hookrightarrow \dot{K}%_{s}^{\alpha_{1},p}F_{\beta }^{s_{1}} \end{equation*} where the…

We extend the definition of weak and strong convergence to sequences of Sobolev-functions whose underlying domains themselves are converging. In contrast to previous works, we do so without ever assuming any sort of reference configuration.…

In this paper we investigate the problem of non-analytic embeddings of Lorentzian manifolds in Ricci-flat semi-Riemannian spaces. In order to do this, we first review some relevant results in the area, and then motivate both the…

In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales. We show that some such results remain valid for metric spaces with non-unique…

In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for the scales of Haj{\l}asz-Triebel-Lizorkin and Haj{\l}asz-Besov spaces in the general context…

We characterize the lack of compactness in the critical embedding of functions spaces $X\subset Y$ having similar scaling properties in the following terms : a sequence $(u_n)_{n\geq 0}$ bounded in $X$ has a subsequence that can be…

For function spaces equipped with Muckenhoupt weights, the validity of continuous Sobolev embeddings in case $p_0\leq p_1$ is characterized. Extensions to Jawerth-Franke embeddings, vector-valued spaces and examples involving some prominent…

Optimal weighted Sobolev-Lorentz embeddings with homogeneous weights in open convex cones are established, with the exact value of the optimal constant. These embeddings are non-compact, and this paper investigates the structure of their…

We give necessary conditions for the existence of a compact manifold locally modelled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and…

We study nuclear embeddings for spaces of Besov and Triebel-Lizorkin type defined on quasi-bounded domains $\Omega\subset {\mathbb R}^d$. The counterpart for such function spaces defined on bounded domains has been considered for a long…

In this paper, we mainly study the compactness and local structure of immersing surfaces in $\mathbb{R}^n$ with local uniform bounded area and small total curvature $\int_{\Sigma\cap B_1(0)} |A|^2$. A key ingredient is a new quantity which…

In this paper we propose a generalization of the Kontsevich--Soibelman conjecture on the degeneration of Hochschild-to-cyclic spectral sequence for smooth and compact DG category. Our conjecture states identical vanishing of a certain map…