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作者：Siebert, B; Tian, G
摘要：We prove that any genus-2 Lefschetz fibration without reducible fibers and with transitive monodromy is holomorphic. The latter condition comprises all cases where the number of singular fibers mu is an element of 10 N is not congruent to 0 modulo 40. This proves a conjecture of the authors in [SiTi1]. An auxiliary statement of independent interest is the holomorphicity of symplectic surfaces in S-2-bundles over S-2, of relative degree <= 7 over the base, and of symplectic surfaces in CP2 of d...
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作者：Klainerman, S; Rodnianski, I
摘要：This is the second in a series of three papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. In this paper we develop the geometric analysis of the Eikonal equation for microlocalized rough Einstein metrics. This is a crucial step in the derivation of ...
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作者：Bianchini, S; Bressan, A
摘要：We consider the Cauchy problem for a strictly hyperbolic, n x n system in one-space dimension: u(t) + A(u)u(x) = 0, assuming that the initial data have small total variation. We show that the solutions of the viscous approximations u(t) + A(u)u(x) = epsilon u(xx) are defined globally in time and satisfy uniform BV estimates, independent of e. Moreover, they depend continuously on the initial data in the L-1 distance, with a Lipschitz constant independent of t, epsilon. Letting epsilon -> 0, th...
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作者：Labourie, F
摘要：Invariant measures for the geodesic flow on the unit tangent bundle of a negatively curved Riemannian manifold are a basic and well-studied subject. This paper continues an investigation into a 2-dimensional analog of this flow for a 3-manifold N. Namely, the article discusses 2-dimensional surfaces immersed into N whose product of principal curvature equals a constant k between 0 and 1, surfaces which are called k-surfaces. The 2-dimensional analog of the unit tangent bundle with the geodesic...
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作者：Derridj, M; Tartakoff, DS
摘要：In [2], J. J. Kohn proves C-infinity hypoellipticity for a sum of squares of complex vector fields which exhibit a large loss of derivatives. Here, we prove analytic hypoellipticity for this operator.
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作者：Bertolini, M; Darmon, H
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作者：Hertz, FR
摘要：We find a class of ergodic linear automorphisms of T-N that are stably ergodic. This class includes all non-Anosov ergodic automorphisms when N = 4. As a corollary, we obtain the fact that all ergodic linear automorphism of T-N are stably ergodic when N <= 5.
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作者：Borodin, A; Olshanski, G
摘要：The infinite-dimensional unitary group U(infinity) is the inductive limit of growing compact unitary groups U(N). In this paper we solve a problem of harmonic analysis on U(infinity) stated in [Ol3]. The problem consists in computing spectral decomposition for a remarkable 4-parameter family of characters of U(infinity). These characters generate representations which should be viewed as analogs of nonexisting regular representation of U(infinity). The spectral decomposition of a character of ...
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作者：Rohde, S; Schramm, O
摘要：SLE kappa is a random growth process based on Loewner's equation with driving parameter a one-dimensional Brownian motion running with speed kappa. This process is intimately connected with scaling limits of percolation clusters and with the outer boundary of Brownian motion, and is conjectured to correspond to scaling limits of several other discrete processes in two dimensions. The present paper attempts a first systematic study of SLE. It is proved that for all kappa not equal 8 the SLE tra...
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作者：Hambleton, I; Pedersen, EK
摘要：the two parts of this paper we prove that the Reidemeister torsion invariants determine topological equivalence of G-representations, for G a finite cyclic group.
