相关论文: The total second variation of Perelman's $\mathcal…

We present a new and simple method for the determination of the pointwise H\"{o}lder exponent of Riemann's function $\sum_{n=1}^{\infty} n^{-2}\sin(\pi n^{2} x)$ at every point of the real line. In contrast to earlier approaches, where…

We investigate recursive properties of certain p-adic Whittaker functions (of which representation densities of quadratic forms are special values). The proven relations can be used to compute them explicitly in arbitrary dimensions,…

We present the general theory of relativity in the language of a non-Riemannian geometry, namely, Weyl geometry. We show that the new mathematical formalism may lead to different pictures of the same gravitational phenomena, by making use…

We study random 2-dimensional complexes in the Linial - Meshulam model and find torsion in their fundamental groups at various regimes. We find a simple algorithmically testable criterion for a subcomplex of a random 2-complex to be…

We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that…

We study the Segal-Bargmann transform on $M(2).$ The range of this transform is characterized as a weighted Bergman space. In a similar fashion Poisson integrals are studied. Using a Gutzmer type formula we characterize the range as a class…

We revisit McLean's second variation formulas for calibrated submanifolds in exceptional geometries, and correct his formulas concerning associative submanifolds and Cayley submanifolds, using a unified treatment based on the (relative)…

We study the SU(2) Witten--Reshetikhin--Turaev invariant for the Seifert fibered homology spheres with M-exceptional fibers. We show that the WRT invariant can be written in terms of (differential of) the Eichler integrals of modular forms…

A new method of constructing a weak coupling expansion of two dimensional (2D) models with an unbroken continuous symmetry is developed. The method is based on an analogy with the abelian XY model, respects the Mermin-Wagner (MW) theorem…

We present a probabilistic argument supporting the application of polar duality, as discussed in our previous work, to express the indeterminacy principle of quantum mechanics. Our approach combines the properties of the Mahler volume of a…

We prove multidimensional integration by parts formulas for generalized fractional derivatives and integrals. The new results allow us to obtain optimality conditions for multidimensional fractional variational problems with Lagrangians…

We construct a generalization of the two-dimensional Wess-Zumino-Witten model on a $2n$-dimensional K\"ahler manifold as a group-valued non-linear sigma model with an anomaly term containing the K\"ahler form. The model is shown to have an…

We study Hermitian metrics with constant second scalar curvature on compact manifolds. We first consider a Yamabe-type problem for the second Bismut scalar curvature under a natural topological condition, and then analyze elliptic equations…

We analyze the finite temperature (T) extension of the Wess-Zumino- Witten functional, discussed in a previous work, to one loop in chiral perturbation theory. As a phenomenological application, we calculate finite temperature corrections…

This note concerns the general formulation by Preiss and Uher of Kestelman's influential result pertaining the change of variable, or substitution, formula for the Riemann integral.

The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values…

In the paper, we first study more general models, where $F$ has constant rank and is based on weak metric structures (introduced by the first author and R. Wolak), which generalize almost complex and almost contact metric $f$-contact…

This paper is a continuation of [2], where we complete our partial proof of the Deser-Schwimmer conjecture on the structure of ``global conformal invariants''. Our theorem deals with such invariants P(g^n) that locally depend only on the…

The usual interpretation of Weyl geometry is modified in two senses. First, both the additive Weyl connection and its variation are treated as (1, 2) tensors under the action of Weyl covariant derivative. Second, a modified covariant…

In our last work, we formulate a Fourier transformation on the infinite-dimensional space of functionals. Here we first calculate the Fourier transformation of infinite-dimensional Gaussian distribution $\exp(-\pi…