Related papers: On M. Mueter's Ph.D. Thesis on Cheeger deformation…
We prove that the groupoid of transformations of rigid structures on surfaces has a finite presentation as a 2-groupoid establishing a result first conjectured by G.Moore and N.Seiberg. An alternative proof was given by B.Bakalov and…
PhD thesis concerning cohomological finiteness conditions of infinite discrete groups. Much of the material in this thesis has also appeared in arXiv:1311.7629, arXiv:1310.6262, arXiv:1311.6156, and arXiv:1207.1597.
Weakly stable constant mean curvature (CMC) hypersurfaces are stable critical points of the area functional with respect to volume preserving deformations. We establish a pointwise curvature estimate (in the non-singular dimensions) and a…
In this paper, we extend Su-Zhang's Cheeger-Mueller type theorem for symmetric bilinear torsions to manifolds with boundary in the case that the Riemannian metric and the non-degenerate symmetric bilinear form are of product structure near…
This article consisted of an elementary introduction to deformation theory of varieties, schemes and manifolds, with some applications to local and global shtukas and fever to Newton polygons of $p$-divisible groups . Soft problems and…
This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions and star-products, following a technique developed earlier, {\it viz\/,} using the unitary…
We establish a link between the behavior of length functions on Teichm\"uller space and the geometry of certain anti de Sitter 3-manifolds. As an application, we give new purely anti de Sitter proofs of results of Teichm\"uller theory such…
We consider the Grothendieck--Teichm\"uller group under a new aspect. Using real algebraic geometry and web theory we show that it preserves dihedral symmetry relations, present in the fundamental groupoids of configuration spaces of marked…
In this paper, we continue the study of $T\bar{T}$ deformation in $d=1$ quantum mechanical systems and propose possible analogues of $J\bar{T}$ deformation and deformation by a general linear combination of $T\bar{T}$ and $J\bar{T}$ in…
The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher-Taylor leaky dielectric model. The main assumption of the…
This is an exposition of the theory of differentiable structures on metric measures spaces, in the sense of Cheeger and Keith.
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…
The purpose of this paper is to investigate applications the covariant derivatives, killing vector fields and to calculate the components of the curvature tensor CGR of the Cheeger-Gromoll metric with respect to adapted frames in a the…
Here (the last paper in a series of four) we end our presentation of the basics of a systematical approach to the differential geometry of a smooth manifold M (supporting a metric field g and a general connection del) which uses the…
This doctoral thesis is a mathematical study of quantum computing, concentrating on two related, but independent topics. First up are dilations, covered in chapter 2. In chapter 3 "diamond, andthen, dagger" we turn to the second topic:…
We give a simple geometric description of all formal deformation quantizations on a K\"ahler manifold $M$ which enjoy the following property of separation of variables into holomorphic and antiholomorphic ones. For each open subset…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
A 4-dimensional Riemannian manifold M, equipped with an additional tensor structure S, whose fourth power is minus identity, is considered. The structure S has a skew-circulant matrix with respect to some basis of the tangent space at a…
These are lecture notes of a course on Calogero-Moser systems and their connections with representation theory and geometry, given by the author in Zurich in May-June 2005.
In a series of papers, Weil initiated the investigation of translation invariant curvature measures of convex bodies, which include as prime examples Federer's curvature measures. In this paper, we continue this line of research by…