相关论文: A Mirzakhani recursion for non-orientable surfaces

In this work, we introduce new families of nonconforming approximation methods for reconstructing functions on general polygonal meshes. These methods are defined using degrees of freedom based on weighted moments of orthogonal polynomials…

The results of this paper are outdated. Finer versions of them will appear elsewhere.

Zernike polynomials are widely used in optics and ophthalmology due to their direct connection to classical optical aberrations. While orthogonal on the unit disk, their application to discrete data or non-circular domains--such as…

We consider the holographic computation of two dimensional conformal field theory partition functions on non-orientable surfaces. We classify the three dimensional geometries that give bulk saddle point contributions to the partition…

We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kahler metrics with constant scalar curvature, and metrics with harmonic curvature. With…

We study a metric version of the simplicial volume on Riemannian manifolds, the Lipschitz simplicial volume, with applications to degree theorems in mind. We establish a proportionality principle and a product inequality from which we…

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

Magnetic particle imaging (MPI) is a medical imaging modality of recent origin, and it exploits the nonlinear magnetization phenomenon to recover the spatially dependent concentration of the nanoparticles. Currently, image reconstruction in…

We develop a recursive computational procedure to efficiently calculate the macroscopic dielectric function of multi-component metamaterials of arbitrary geometry and composition within the long wavelength approximation. Although the…

Given integers $g,n \geq 0$ satisfying $2-2g-n < 0$, let $\mathcal{M}_{g,n}$ be the moduli space of connected, oriented, complete, finite area hyperbolic surfaces of genus $g$ with $n$ cusps. We study the global behavior of the Mirzakhani…

This paper develops matrix-multiplication-based iterative refinement for diagonalizable non-Hermitian eigendecompositions. The main theory concerns simple eigenvalues and distinguishes two input regimes. In the right-only regime, where only…

Non-linear filtering approaches allow to obtain decompositions of images with respect to a non-classical notion of scale, induced by the choice of a convex, absolutely one-homogeneous regularizer. The associated inverse scale space flow can…

We study extensions of the measure of maximal entropy to suitable compactifications of the parameter space and the moduli space of rational maps acting on the Riemann sphere. For parameter space, we consider a space which resolves the…

We study the differential inclusion $Du\in K$, where $K$ is an unbounded and rotationally invariant subset of the real symmetric $3\times 3$ matrices. We exhibit a subset of all possible average fields. The corresponding microgeometries are…

We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained…

We find the density matrix corresponding to the vacuum state of a massless Dirac field in two dimensions reduced to a region of the space formed by several disjoint intervals. We calculate explicitly its spectral decomposition. The…

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency…

Nonuniform tubular neighborhoods of curves in Euclidean n-space are studied by using weighted distance functions and generalizing the normal exponential map. Different notions of injectivity radii are introduced to investigate singular but…

We study Hodge Integrals on Moduli Spaces of Admissible Covers. Motivation for this work comes from Bryan and Pandharipande's recent work on the local GW theory of curves, where analogouos intersection numbers, computed on Moduli Spaces of…

We give necessary conditions on complete embedded \cmc surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are two-dimensional varieties in the moduli spaces of general \cmc surfaces. We…