-
作者：Luo, Tian-Wen; Yu, Pin
作者单位：South China Normal University; Tsinghua University
摘要：We study the resolution of discontinuous singularities in gas dynamics via rarefaction waves. The mechanism is well-understood in the one-dimensional case. We will prove the nonlinear stability of the Riemann problem for multi-dimensional isentropic Euler equations in the regime of rarefaction waves. The proof relies on the new energy estimates without loss of derivatives. We also give a detailed geometric description of the rarefaction wave fronts. This is the first paper in the series which ...
-
作者：Chaika, Jon; Smillie, John; Weiss, Barak
作者单位：Rice University; University of Warwick; Tel Aviv University
摘要：We introduce a 'tremor' deformation on strata of translation surfaces. Using it, we give new examples of behaviors of horo cycle flow orbits Uq in strata of translation surfaces. In the genus 2 stratum H(1, 1) we find orbits Uq which are generic for a measure whose support is strictly contained in Uq and find orbits which are not generic for any measure. We also describe a horo cycle orbit-closure whose Hausdorff dimension is not an integer.
-
作者：Eichinger, Benjamin; Lukic, Milivoje; Simanek, Brian
作者单位：Lancaster University; Technische Universitat Wien; Rice University; Baylor University
摘要：We describe an approach to universality limits for orthogonal polynomials on the real line which is completely local and uses only the boundary behavior of the Weyl m-function at the point. We show that bulk universality of the Christoffel-Darboux kernel holds for any point where the imaginary part of the m-function has a positive finite nontangential limit. This approach is based on studying a matrix version of the Christoffel- Darboux kernel and the realization that bulk universality for thi...
-
作者：Schwartz, R. I. C. H. A. R. D. EvAN
作者单位：Brown University
摘要：We prove that a smooth embedded paper Moebius band must have aspect ratio greater than \/3. We also prove that any sequence of smooth embedded paper Moebius bands whose aspect ratio converges to \/3 must converge, up to isometry, to the triangular Moebius band. These results answer the mimimum aspect ratio question discussed by W. Wunderlich in 1962 and prove the more specific conjecture of B. Halpern and C. Weaver from 1977.
-
作者：Jaikin-Zapirain, Andrei; Linton, Marco
作者单位：Autonomous University of Madrid; Universidad Carlos III de Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); Complutense University of Madrid; CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT); Autonomous University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); Universidad Carlos III de Madrid; Complutense University of Madrid; CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT)
摘要：We prove that one-relator groups are coherent, solving a well-known problem of Gilbert Baumslag. Our proof strategy is readily applicable to many classes of groups of cohomological dimension two. We show that fundamental groups of two complexes with non-positive immersions are homologically coherent, we show that groups with staggered presentations and many Coxeter groups are coherent and we show that group algebras over fields of characteristic zero of groups with reducible presentations with...
-
作者：Yuan, Xinyi
作者单位：Peking University
摘要：In this paper, we construct the admissible canonical bundle of a quasi-projective family of curves, prove that it is a big adelic line bundle when the family has maximal variation, and apply it to prove a uniform Bogomolovtype theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Vojta, Dimitrov-Gao-Habegger and Kuhne. Our treatment is based on the theory of adelic line bundles on quasi-projective varieties r...
-
作者：Luo, Tian-Wen; Yu, Pin
作者单位：South China Normal University; Tsinghua University
摘要：This is the second paper in a series studying the nonlinear stability of rarefaction waves in multi-dimensional gas dynamics. We construct initial data near singularities in the rarefaction wave region and, combined with the a priori energy estimates from the first paper, demonstrate that any smooth perturbation of constant states on one side of the diaphragm in a shock tube can be connected to a centered rarefaction wave. We apply this analysis to study multi-dimensional perturbations of the ...
-
作者：Luo, Tian-Wen; Yu, Pin
作者单位：South China Normal University; Tsinghua University
摘要：We study the resolution of discontinuous singularities in gas dynamics via rarefaction waves. The mechanism is well-understood in the one-dimensional case. We will prove the nonlinear stability of the Riemann problem for multi-dimensional isentropic Euler equations in the regime of rarefaction waves. The proof relies on the new energy estimates without loss of derivatives. We also give a detailed geometric description of the rarefaction wave fronts. This is the first paper in the series which ...
-
作者：Chaika, Jon; Smillie, John; Weiss, Barak
作者单位：Rice University; University of Warwick; Tel Aviv University
摘要：We introduce a 'tremor' deformation on strata of translation surfaces. Using it, we give new examples of behaviors of horo cycle flow orbits Uq in strata of translation surfaces. In the genus 2 stratum H(1, 1) we find orbits Uq which are generic for a measure whose support is strictly contained in Uq and find orbits which are not generic for any measure. We also describe a horo cycle orbit-closure whose Hausdorff dimension is not an integer.
-
作者：Newton, James; Thorne, Jack
作者单位：University of Oxford; University of Cambridge
摘要：Let F be a totally real field. We prove the existence of all symmetric power liftings of those cuspidal automorphic representations of GL2(AF) associated to Hilbert modular forms of regular weight.
