Related papers: Small resolutions of special three-dimensional var…
This is a review paper of the role of Carleman estimates in the theory of Multidimensional Coefficient Inverse Problems since the first inception of this idea in 1981.
Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.
This note provides a deeper understanding of the main results obtained in the author's 2007 DPDE paper \cite{Xiao}.
Given a nonlinear dispersive equation which admits a scaling invariance, there may exist self-similar solutions. In this work, we present a systematic approach for the construction of small-amplitude self-similar solutions, together with…
The purpose of this paper is: 1) to explain the Seiberg-Witten invariants, 2) to show that - on a K\"ahler surface - the solutions of the monopole equations can be interpreted as algebraic objects, namely effective divisors, 3) to give - as…
All complex $3$-dimensional nilalgebras were described. As a corollary, all degenerations in the variety of complex $3$-dimensional nilalgebras were obtained.
New version of my 1998 article. The method of proof of the main results follows the original, but there are many simplifications/streamlining of arguments, especially Lemma 3.6 (new Lemma 3.7). Fixed small error in proof of lower bound for…
We develop a variational technique for some wide classes of nonlinear evolutions. The novelty here is that we derive the main information directly from the corresponding Euler-Lagrange equations. In particular, we prove that not only the…
In this paper, we describe on the one hand, all relative minimal models Y of a minuscule Schubert variety X using some combinatorics on quivers and we prove that the morphism from Y to X is small (in the sense of intersection cohomology).…
This is an English translation of "The Problem of Resolvents and Critical Manifolds" by Tschebotarow/Chebotarev. In this article, Chebotarev explains his work on resolvent problems using critical manifolds. The current ideas of resolvent…
In this paper, we obtain dispersion relations corresponding to plane wave solutions in various Lorentz-breaking extensions of gravity with dimensions 3, 4, 5 and 6. We demonstrate that these dispersion relations display an usual…
This is an English translation of G.N. Chebotarev's paper "On The Klein-Hilbert Resolvent Problem" which was originally written in Russian and published in Izvestiya Kazan. Fiz. Mat. Obshch., 6 (1932-1933), 5-22. In this article, Chebotarev…
This is a short note about a chapter in the author's bachelor thesis regarding a paper by Ford concerning a conjecture by Erd\H{o}s.
The main result of this paper was already obtained in the paper `Some Remarks on the Geometry of Austere Manifolds', by Robert L. Bryant.
The lower dimensional Busemann-Petty problem asks whether origin-symmetric convex bodies in R^n with smaller volume of all k-dimensional sections necessarily have smaller volume. The answer is negative for k>3. The problem is still open for…
A new technique was recently developed to approximate the solution of the Schroedinger equation. This approximation (dubbed ERS) is shown to yield a better accuracy than the WKB-approximation. Here, we review the ERS approximation and its…
We generalize Werner's defect formula for nodal hypersurfaces in $\mathbb P^{4}$ to the case of a nodal complete intersection threefold.
This is an introduction to small divisors problems. The material treated in this book was brought together for a PhD course I tought at the University of Pisa in the spring of 1999. Here is a Table of Contents: Part I One Dimensional Small…
The problem of investigation of the simplest n-dimensional continued fraction in the sense of Klein for n>2 was posed by V.Arnold. The answer for the case of n=2 can be found in the works of E.Korkina and G.Lachaud. In present work we study…
We investigate a variant of Wirsing's problem on approximation to a real number by real algebraic numbers of degree exactly $n$. This has been studied by Bugeaud and Teulie. We improve their bounds for degrees up to $n=7$. Moreover, we…