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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...
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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 ...
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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 ...
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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.
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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...
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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 ...
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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 ...
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作者：Yang, Lei
作者单位：Institute for Advanced Study - USA; National University of Singapore
摘要：In this paper, we will prove an effective version of Ratner's equidistribution theorem for unipotent orbits in SL(3, R)/SL(3, Z) with a natural Diophantine condition.
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作者：Ruhstorfer, Lucas
作者单位：University of Wuppertal
摘要：In this paper we consider the inductive Alperin-McKay condition for quasi-isolated 2-blocks of exceptional groups of Lie type. Thereby, we complete the proof of the Alperin-McKay conjecture and Brauer's height zero conjecture for the prime 2.
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作者：Dafermos, Mihalis; Luk, Jonathan
作者单位：Princeton University; University of Cambridge; Stanford University
摘要：We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations defined on a hypersurface already within the black hole interior, representing the expected geometry just inside the event horizon. We prove that, for all such data, the maximal Cauchy evolution can be extended across a non-trivial piece of Cauchy horizon as a Lor...
