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A compactness theorem for volume-constrained almost-critical points of elliptic integrands is proven. The result is new even for the area functional, as almost-criticality is measured in an integral rather than in a uniform sense. Two main…

In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the…

We continue a study of the relations between two consequences of the Continuum Hypothesis discovered by Waclaw Sierpinski, concerning uniform continuity of continuous functions and uniform convergence of sequences of real-valued functions,…

In this article we prove a multidimensional version of the Nazarov lemma. The proof is based on an appropriate generalisation of the regularised system of intervals introduced by Havin, Nazarov and Mashreghi to several dimensions.

We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.

We investigate the famous conjecture by Erd\H os-Simonovits and Sidorenko using information theory. Our method gives a unified treatment for all known cases of the conjecture and it implies various new results as well. Our topological type…

In this paper we propose generalizations of the Sokolov-Ternov and Unruh effects, and discuss the possibility to measure them on different experiments.

In this note we will review the most important results and questions related to Chern conjecture and isoparametric hypersurfaces, as well as their interactions and applications to various aspects in mathematics.

A dimension allowing in particular to state necessary and sufficient conditions of the Morse-Sard Theorem for real valued functions is introduced.

Classical H.Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H.Minkowski uniqueness theorem due to A.D.Alexandrov are extended to a…

We give a brief review of recent developments in five-dimensional theories of spacetime and highlight their geometrical structure mainly in connection with the Campbell-Magaard theorem.

We discuss Kadison's Carpenter's Theorems in the context of majorisation, and we offer a new proof of his "Theorem 15", that characterizes the set of diagonals of orthogonal projections.

We discuss some recent results by Parini and Ruf on a Moser-Trudinger type inequality in the setting of Sobolev-Slobodeckij spaces in dimension one. We push further their analysis considering the inequality on the whole $\mathbb{R}$ and we…

We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.

We study the number of (set-theoretically) defining equations of Segre products of projective spaces times certain projective hypersurfaces, extending results by Singh and Walther. Meanwhile, we prove some results about the cohomological…

We clarify and extend insights from Lavrentiev's seminal paper. We examine the original theorem dealing with the absence of the Lavrentiev phenomenon, a cornerstone issue in the calculus of variations. We point out some inconsistencies in…

In this paper we study an overdetermined problem which is directly related to the well known torsion problem studied by J. Serrin. A perturbed version of the latter is tackled by using asymptotic series as well as tools borrowed from the…

Given a division ring K containing the field k in its center and A,B two finite subsets of K\{0}, we give some analogues of Pl\"unnecke and Kneser theorems for the dimension of the k-linear span of the Minkowski product AB in terms of the…

In this paper we prove some new symmetry results for the extremals of the Caffarelli-Kohn-Nirenberg inequalities, in any dimension larger or equal than two.

We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…