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作者：Hodgson, CD; Kerckhoff, SP
摘要：This paper gives a quantitative version of Thurston's hyperbolic Dehn surgery theorem. Applications include the first universal bounds on the number of nonhyperbolic Dehn fillings on a cusped hyperbolic 3-manifold, and estimates on the changes in volume and core geodesic length during hyperbolic Dehn filling. The proofs involve the construction of a family of hyperbolic cone-manifold structures, using infinitesimal harmonic deformations and analysis of geometric limits.
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作者：Etnyre, JB; Honda, K
摘要：We study Legendrian knots in a cabled knot type. Specifically, given a topological knot type K, we analyze the Legendrian knots in knot types obtained from K by cabling, in terms of Legendrian knots in the knot type K. As a corollary of this analysis, we show that the (2,3)-cable of the (2,3)-torus knot is not transversely simple and moreover classify the transverse knots in this knot type. This is the first classification of transverse knots in a non-transversely-simple knot type. We also cla...
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作者：Green, B
摘要：We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a restriction theorem for the primes.
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作者：White, B
摘要：This paper proves curvature bounds for mean curvature flows and other related flows in regions of spacetime where the Gaussian densities are close to 1.
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作者：Papasoglu, P
摘要：We show that a finitely presented one-ended group which is not commensurable to a surface group splits over a two-ended group if and only if its Cayley graph is separated by a quasi-line. This shows in particular that splittings over two-ended groups are preserved by quasi-isometries.
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作者：Smith, HF; Tataru, D
摘要：This article is concerned with local well-posedness of the Cauchy problem for second order quasilinear hyperbolic equations with rough initial data. The new results obtained here are sharp in low dimension.
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作者：Eastwood, M
摘要：We identify the symmetry algebra of the Laplacian on Euclidean space as an explicit quotient of the universal enveloping algebra of the Lie algebra of conformal motions. We construct analogues of these symmetries on a general conformal manifold.
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作者：Guedj, V
摘要：Let X be a projective manifold and f : X -> X a. rational mapping with large topological degree, d(t) > lambda(k-1)(f) := the (k - 1)(th) dynamical degree of f. We give an elementary construction of a probability measure mu(f) such that d(t)(-n)(f(n))*Theta -> mu(f) for every smooth probability measure Theta on X. We show that every quasiplurisubharmonic function is mu(f)-integrable. In particular mu(f) does not charge either points of indeterminacy or pluripolar sets, hence mu(f) is f-invaria...
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作者：Boyer, CP; Galicki, K; Kollár, J
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作者：Bartal, Y; Linial, N; Mendel, M; Naor, A
摘要：The main question studied in this article may be viewed as a nonlinear analogue of Dvoretzky's theorem in Banach space theory or as part of Ramsey theory in combinatorics. Given a finite metric space on n points, we seek its subspace of largest cardinality which can be embedded with a given distortion in Hilbert space. We provide nearly tight upper and lower bounds on the cardinality of this subspace in terms of n and the desired distortion. Our main theorem states that for any epsilon > 0, ev...
