-
作者：Ghazouani, Selim
作者单位：Universite Paris Saclay
摘要：In this article we study local rigidity properties of generalised interval exchange maps using renormalisation methods. We study the dynamics of the renormalisation operator R acting on the space of C-3-generalised interval exchange transformations at fixed points (which are standard periodic type IETs). We show that R is hyperbolic and that the number of unstable direction is exactly that predicted by the ergodic theory of IETs and the work of Forni and Marmi-Moussa-Yoccoz. As a consequence w...
-
作者：Meeks, William H., III; Tinaglia, Giuseppe
作者单位：University of Massachusetts System; University of Massachusetts Amherst; University of London; King's College London
摘要：We describe the lamination limits of sequences of compact disks M-n embedded in R-3 with constant mean curvature H-n, when the boundaries of these disks tend to infinity. This theorem generalizes to the non-zero constant mean curvature case Theorem 0.1 by Colding and Minicozzi (Ann Math 160:573-615, 2004) for minimal disks. We apply this theorem to prove the existence of a chord arc result for compact disks embedded in R-3 with constant mean curvature; this chord arc result generalizes Theorem...
-
作者：Pigati, Alessandro; Stern, Daniel
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Princeton University
摘要：Given a Hermitian line bundle L -> M over a closed, oriented Riemannian manifoldM, we study the asymptotic behavior, as epsilon -> 0, of couples(u(epsilon), del(epsilon)) critical for the rescalings E epsilon(u, del)= (M)integral(vertical bar del u vertical bar(2)+epsilon(2)vertical bar F-del vertical bar(2)+1/4 epsilon(2)(1-vertical bar u vertical bar(2))(2)) of the self-dual Yang-Mills-Higgs energy, whereuis a section of Land del is a Hermitian connection on L with curvature F-del. Under the...
-
作者：Daskalopoulos, Georgios; Mese, Chikako
作者单位：Brown University; Johns Hopkins University
摘要：We prove the holomorphic rigidity conjecture of Teichmuller space which loosely speaking states that the action of the mapping class group uniquely determines theTeichmuller space as a complex manifold. The method of proof is through harmonicmaps. We prove that the singular set of a harmonic map from a smooth n-dimensional Riemannian domain to theWeil-Petersson completion T of Teichmuller space has Hausdorff dimension at most n - 2, and moreover, u has certain decay near the singular set. Comb...
-
作者：Gwynne, Ewain; Miller, Jason
作者单位：University of Cambridge
摘要：We show that for each gamma is an element of (0, 2), there is a unique metric (i.e., distance function) associated with gamma-Liouville quantum gravity (LQG). More precisely, we show that for the whole-plane Gaussian free field (GFF) h, there is a unique random metric D-h associated with the Riemannian metric tensor e(gamma h)(dx(2) + dy(2)) on C which is characterized by a certain list of axioms: it is locally determined by h and it transforms appropriately when either adding a continuous fun...
-
作者：Avramidi, Grigori; Okun, Boris; Schreve, Kevin
作者单位：Max Planck Society; University of Wisconsin System; University of Wisconsin Milwaukee; University of Chicago
摘要：We compute the mod p homology growth of residual sequences of finite index normal subgroups of right-angled Artin groups. We find examples where this differs from the rational homology growth, which implies the homology of subgroups in the sequence has lots of torsion. More precisely, the homology torsion grows exponentially in the index of the subgroup. For odd primes p, we construct closed locally CAT(0) manifolds with nonzero mod p homology growth outside the middle dimension. These example...
-
作者：Levinson, Jake; Purbhoo, Kevin
作者单位：Simon Fraser University; University of Waterloo
摘要：We prove a generalization of the Shapiro-Shapiro conjecture on Wronskians of polynomials, allowing the Wronskian to have complex conjugate roots. We decompose the real Schubert cell according to the number of real roots of the Wronski map, and define an orientation of each connected component. For each part of this decomposition, we prove that the topological degree of the restricted Wronski map is given as an evaluation of a symmetric group character. In the case where all roots are real, thi...
-
作者：Davison, Ben; Mandel, Travis
作者单位：University of Edinburgh; University of Oklahoma System; University of Oklahoma - Norman
摘要：We construct quantum theta bases, extending the set of quantum cluster monomials, for various versions of skew-symmetric quantum cluster algebras. These bases consist precisely of the indecomposable universally positive elements of the algebras they generate, and the structure constants for their multiplication are Laurent polynomials in the quantum parameter with non-negative integer coefficients, proving the quantum strong cluster positivity conjecture for these algebras. The classical limit...
-
作者：Larson, Hannah K.
摘要：Let f : C -> P-1 be a degree k genus g cover. The stratification of line bundles L is an element of Pic(d) (C) by the splitting type of f(*)L is a refinement of the stratification by Brill-Noether loci W-d(r) (C). We prove that for general degree k covers, these strata are smooth of the expected dimension. In particular, this determines the dimensions of all irreducible components of W-d(r)(C) for a general k-gonal curve (there are often components of different dimensions), extending results o...
-
作者：Fraczyk, Mikolaj
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
摘要：We show that every sequence of torsion-free arithmetic congruence lattices in PGL(2, R) or PGL(2, C) satisfies a strong quantitative version of the limit multiplicity property. We deduce that for R > 0 in certain range, growing linearly in the degree of the invariant trace field, the volume of the R-thin part of any congruence arithmetic hyperbolic surface or congruence arithmetic hyperbolic 3-manifold M is of order at most Vol(M)(11/12). As an application we prove Gelander's conjecture on hom...
