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作者：Bigelow, Stephen; Morrison, Scott; Peters, Emily; Snyder, Noah
作者单位：University of California System; University of California Santa Barbara; Australian National University; Massachusetts Institute of Technology (MIT); Indiana University System; Indiana University Bloomington
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作者：Gerard-Varet, David; Masmoudi, Nader
作者单位：Universite Paris Cite; Sorbonne Universite; New York University
摘要：This paper deals with the homogenization of elliptic systems with a Dirichlet boundary condition, when the coefficients of both the system and the boundary data are epsilon-periodic. We show that, as epsilon -> 0, the solutions converge in L-2 with a power rate in epsilon, and identify the homogenized limit system. Due to a boundary layer phenomenon, this homogenized system depends in a non-trivial way on the boundary. Our analysis answers a longstanding open problem, raised for instance in [6...
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作者：Colding, Tobias Holck
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We prove three new monotonicity formulas for manifolds with a lower Ricci curvature bound and show that they are connected to rate of convergence to tangent cones. In fact, we show that the derivative of each of these three monotone quantities is bounded from below in terms of the Gromov-Hausdorff distance to the nearest cone. The monotonicity formulas are related to the classical Bishop-Gromov volume comparison theorem and Perelman's celebrated monotonicity formula for the Ricci flow. We will...
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作者：Namazi, Hossein; Souto, Juan
作者单位：University of Texas System; University of Texas Austin; University of British Columbia
摘要：We give a complete proof of the Bers-Sullivan-Thurston density conjecture. In the light of the ending lamination theorem, it suffices to prove that any collection of possible ending invariants is realized by some algebraic limit of geometrically finite hyperbolic manifolds. The ending invariants are either Riemann surfaces or filling laminations supporting Masur domain measured laminations and satisfying some mild additional conditions. With any set of ending invariants we associate a sequence...
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作者：Bainbridge, Matt; Moeller, Martin
作者单位：Indiana University System; Indiana University Bloomington; Goethe University Frankfurt
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作者：Poltoratski, Alexei
作者单位：Texas A&M University System; Texas A&M University College Station
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作者：Matui, Hiroki; Sato, Yasuhiko
作者单位：Chiba University; Kyoto University
摘要：For any unital separable simple infinite-dimensional nuclear C (au)-algebra with finitely many extremal traces, we prove that -absorption, strict comparison and property (SI) are equivalent. We also show that any unital separable simple nuclear C (au)-algebra with tracial rank zero is approximately divisible, and hence is -absorbing.
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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
