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作者：Viklund, Fredrik Johansson; Lawler, Gregory F.
作者单位：Columbia University; University of Chicago; University of Chicago
摘要：The tip multifractal spectrum of a 2-dimensional curve is one way to describe the behavior of the uniformizing conformal map of the complement near the tip. We give the tip multifractal spectrum for a Schramm-Loewner evolution (SLE) curve, we prove that the spectrum is valid with probability 1, and we give applications to the scaling of harmonic measure at the tip.
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作者：Barbasch, Dan; Ciubotaru, Dan; Trapa, Peter E.
作者单位：Cornell University; Utah System of Higher Education; University of Utah
摘要：We define an analogue of the Casimir element for a graded affine Hecke algebra , and then introduce an approximate square-root called the Dirac element. Using it, we define the Dirac cohomology H (D) (X) of an -module X, and show that H (D) (X) carries a representation of a canonical double cover of the Weyl group . Our main result shows that the -structure on the Dirac cohomology of an irreducible -module X determines the central character of X in a precise way. This can be interpreted as p-a...
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作者：Christensen, Erik; Sinclair, Allan M.; Smith, Roger R.; White, Stuart A.; Winter, Wilhelm
作者单位：University of Copenhagen; University of Edinburgh; Texas A&M University System; Texas A&M University College Station; University of Glasgow; University of Munster
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作者：Cortinas, Guillermo; Thom, Andreas
作者单位：University of Buenos Aires; Leipzig University
摘要：We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, we prove a parameterized version of a theorem by Joseph Gubeladze; we show that if M is a countable, abelian, cancellative, torsion-free, semi-normal monoid, and X is contractible, then every finitely generated projective module over C(X)[M] is free. The particular case giv...
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作者：Klainerman, Sergiu; Rodnianski, Igor
作者单位：Princeton University
摘要：In a recent important breakthrough D. Christodoulou has solved a long standing problem of General Relativity of evolutionary formation of trapped surfaces in the Einstein-vacuum space-times. He has identified an open set of regular initial conditions on an outgoing null hypersurface (both finite and at past null infinity) leading to a formation a trapped surface in the corresponding vacuum space-time to the future of the initial outgoing hypersurface and another incoming null hypersurface with...
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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：Berman, Robert; Boucksom, Sebastien; Nystrom, David Witt
作者单位：Chalmers University of Technology; University of Gothenburg; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：Building on [BB1] we prove a general criterion for convergence of (possibly singular) Bergman measures towards pluripotential-theoretic equilibrium measures on complex manifolds. The criterion may be formulated in terms of the growth properties of the unit-balls of certain norms on holomorphic sections, or equivalently as an asymptotic minimization property for generalized Donaldson L-functionals. Our result settles in particular a well-known conjecture in pluripotential theory concerning the ...
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作者：Tao, Terence; Vu, Van
作者单位：University of California System; University of California Los Angeles; Rutgers University System; Rutgers University New Brunswick
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作者：Cheeger, Jeff; Kleiner, Bruce; Naor, Assaf
作者单位：New York University
