Related papers: Excess decay for minimizing hypercurrents mod $2Q$

We consider a $\pi_{1}$--injective immersion $f:\Sigma\to M$ from a compact surface $\Sigma$ to a hyperbolic 3--manifold $M$. Let $\Gamma$ denote the copy of $\pi_{1}\Sigma$ in $\mathrm{Isom}({\mathbb{H}}^{3})$ induced by the immersion and…

We present a local computation of deformations of the tangent bundle for a resolved orbifold singularity C^d/G. These correspond to (0,2)-deformations of (2,2)-theories. A McKay-like correspondence is found predicting the dimension of the…

We show that for a generic $8$-dimensional Riemannian manifold with positive Ricci curvature, there exists a smooth minimal hypersurface. Without the curvature condition, we show that for a dense set of 8-dimensional Riemannian metrics…

We propose to use residual parafermions of the overscreened Kondo effect for topological quantum computation. A superconducting proximity gap of $\Delta<T_K$ can be utilized to isolate the parafermion from the continuum of excitations and…

We perform a heat kernel asymptotics analysis of the nonperturbative superpotential obtained from wrapping of an M2-brane around a supersymmetric noncompact three-fold embedded in a (noncompact) G_2-manifold as obtained in [1], the…

We show that in the model obtained by iteratively pseudo-intersecting a Ramsey ultrafilter via a length-$\omega_2$ countable support iteration of restricted Mathias forcing over a ground model satisfying $\textsf{CH}$, there is a unique…

This paper addresses some questions about dimension theory for P-minimal structures. We show that, for any definable set A, the dimension of the frontier of A is strictly smaller than the dimension of A itself, and that A has a…

The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…

For convex co-compact hyperbolic quotients $X=\Gamma\backslash\hh^{n+1}$, we analyze the long-time asymptotic of the solution of the wave equation $u(t)$ with smooth compactly supported initial data $f=(f_0,f_1)$. We show that, if the…

We study the structure of Gromov-Hausdorff limits of sequences of Riemannian manifolds $\{(M_\alpha^n,g_\alpha)\}_{\alpha \in A}$ whose Ricci curvature satisfies a uniform Kato bound. We first obtain Mosco convergence of the Dirichlet…

A basic question in submanifold theory is whether a given isometric immersion $f\colon M^n\to\R^{n+p}$ of a Riemannian manifold of dimension $n\geq 3$ into Euclidean space with low codimension $p$ admits, locally or globally, a genuine…

A bound on the angle gamma of the unitarity triangle is derived using experimental information on the CP-averaged branching ratios for the rare decays B^+- -> pi^+- K^0 and B^+- -> pi^0 K^+-. The theoretical description is cleaner than the…

Strong mesonic decays are studied in the framework of the 't Hooft model for the two-dimensional QCD in the axial gauge. Special attention is payed to the processes with pions in the final state involved and the low energy theorems have…

We study the properties of sets $\Sigma$ which are the solutions of the maximal distance minimizer problem, i.e. of sets having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets $\Sigma \subset…

The moduli space of Riemann surfaces of genus $g\geq 2$ is (up to a finite \'etale cover) a complex manifold and so it makes sense to speak of its Dolbeault cohomological dimension. The conjecturally optimal bound is $g-2$. This expectation…

We address a number of puzzles relating to the proposed formulae for the degeneracies of dyons in orbifold compactifications of the heterotic string to four dimensions with $N =4$ supersymmetry. The partition function for these dyons is…

For a smooth $k$-dimensional submanifold $\Sigma$ of a $d$-dimensional compact Riemannian manifold $M$, we extend the $L^p(\Sigma)$ restriction bounds of Burq-G\'erard-Tzvetkov -- originally proved for individual Laplace--Beltrami…

Superconducting quantum circuits must be designed carefully to avoid dissipation from coupling to external control circuitry. Here we introduce the concept of current transformation to quantify coupling to the environment. We test this…

We investigate quantum corrections to the moduli space for hypermultiplets for type IIA near a conifold singularity. We find a unique quantum deformation based on symmetry arguments which is consistent with a recent conjecture. The…

Supercurrents, as introduced by Lagerberg, were mainly motivated as a way to study tropical varieties. Here we will associate a supercurrent to any smooth submanifold of $\R^n$. Positive supercurrents resemble positive currents in complex…