Related papers: H\"older regularity for the spectrum of translatio…
We give a simple proof for the rotational symmetry of ancient solutions of Ricci flow on surfaces. As a consequence we obtain a simple proof of some results of P.Daskalopoulos, R.Hamilton and N.Sesum on the a priori estimates for the…
Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat $3$-manifolds which we call translation prisms. Using ideas of Furstenberg and Veech, we connect results about weak mixing properties of…
We consider a surface diffusion flow of the form $V=\partial_s^2f(-\kappa)$ with a strictly increasing smooth function $f$ typically, $f(r)=e^r$, for a curve with arc-length parameter $s$, where $\kappa$ denotes the curvature and $V$…
In this contribution we obtain partial $C^{0,\alpha}$-regularity for bounded solutions of a certain class of cross-diffusion systems, which are strongly coupled, degenerate quasilinear parabolic systems. Under slightly more restrictive…
In this work we study strong spectral properties of Ruelle transfer operators related to Gibbs measures for contact Anosov flows. As a consequence we establish exponential decay of correlations for H\"older observables with respect to any…
We prove by methods of harmonic analysis a result on existence of solutions for twisted cohomological equations on translation surfaces with loss of derivatives at most 3+ in Sobolev spaces. As a consequence we prove that product…
In this paper we investigate Abel maps on normal surface singularities described in \cite{NNI}. We investigate the affine version of the class of the images of Abel maps on normal surface singularities. More precisely we consider the…
We define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This $G$-equivariant spectral flow shares…
We deal with solitons of the mean curvature flow. The definition of \textit{translating solitons on a light-like direction} in Minkowski 3-space is introduced. Firstly, we classify those which are graphical, \textit{translation surfaces},…
We investigate versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings, for other classes of varieties. We first obtain analogues for certain Fano threefolds. We use these results to prove the…
In this paper, we investigate the moduli of surfaces of general type admitting genus 2 fibrations with irregularity q = g_b + 1, where g_b >= 2 is the genus of the base. We prove that smooth fibrations are parametrized by a unique component…
We establish the existence and uniqueness of some smooth accelerating transonic flows governed by the three dimensional steady compressible Euler equations with an external force in cylinders with arbitrary cross sections, which include…
In this paper we prove a general theorem concerning the number of translation classes of curves of genus $g$ belonging to a fixed cohomology class in a polarized abelian variety of dimension $g$. For $g = 2$ we recover results of G\"ottsche…
We introduce a "tremor" deformation on strata of translation surfaces. Using it, we give new examples of behaviors of horocycle flow orbits in strata of translation surfaces. In the genus two stratum with two singular points, we find orbits…
We consider a wide class of fully nonlinear integro-differential equations that degenerate when the gradient of the solution vanishes. By using compactness and perturbation arguments, we give a complete characterization of the regularity of…
We write down an explicit operator on the chiral de Rham complex of a Calabi-Yau variety $X$ which intertwines the usual $\mathcal{N}=2$ module structure with its twist by the spectral flow automorphism of the $\mathcal{N}=2$, producing the…
We investigate the gradient flow of the $L^2$ norm of the Riemannian curvature on surfaces. We show long time existence with arbitrary initial data, and exponential convergence of the volume normalized flow to a constant scalar curvature…
We prove that every homogeneous flow on a finite-volume homogeneous manifold has countably many independent invariant distributions unless it is conjugate to a linear flow on a torus. We also prove that the same conclusion holds for every…
Investigation of physics on two-dimensional curved surface has significant meaning in study of general relativity, inasmuch as its realizability in experimental analogy and verification of faint gravitational effects in laboratory. Several…
We introduce boundary quotients and present a framework for learning densities on manifolds that arise as boundary quotients of simpler domains. We show that this framework can be used to construct normalizing flows on quotient manifolds…