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作者:Potapov, Denis; Sukochev, Fedor
作者单位:University of New South Wales Sydney
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作者:Astala, Kari; Jones, Peter; Kupiainen, Antti; Saksman, Eero
作者单位:University of Helsinki; Yale University
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作者:Cheeger, Jeff; Kleiner, Bruce; Naor, Assaf
作者单位:New York University
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作者:Gekhtman, Michael; Shapiro, Michael; Vainshtein, Alek
作者单位:University of Notre Dame; Michigan State University; University of Haifa; University of Haifa
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作者:Varvaruca, Eugen; Weiss, Georg S.
作者单位:University of Reading; Heinrich Heine University Dusseldorf
摘要:We consider the Stokes conjecture concerning the shape of extreme 2-dimensional water waves. By new geometric methods including a non-linear frequency formula, we prove the Stokes conjecture in the original variables. Our results do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity. Part of our results extends to the mathematical problem in higher dimensions.
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作者:Benedetti, Bruno; Ziegler, Guenter M.
作者单位:Free University of Berlin
摘要:Durhuus and Jonsson (1995) introduced the class of locally constructible (LC) 3-spheres and showed that there are only exponentially many combinatorial types of simplicial LC 3-spheres. Such upper bounds are crucial for the convergence of models for 3D quantum gravity. We characterize the LC property for d-spheres (the sphere minus a facet collapses to a (d-2)-complex) and for d-balls. In particular, we link it to the classical notions of collapsibility, shellability and constructibility, and ...