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作者：Moreira, CGTD; Yoccoz, JC
摘要：In this paper we prove a conjecture by J. Palis according to which the arithmetic difference of generic pairs of regular Cantor sets on the line either has zero Lebesgue measure or contains an interval. More precisely, we prove that if the sum of the Hausdorff dimensions of two regular Cantor sets is bigger than one then, in almost all cases, there are translations of them whose intersection persistently has Hausdorff dimension.
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作者：Harvey, FR; Lawson, HB Jr
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作者：Krikorian, RL
摘要：We prove that given ce in a set of total (Haar) measure in T-1 = R/Z, the set of A epsilon C-infinity (T-1, SU (2)) for which the skew-product system (a, A) : T-1 x SU(2) --> T-1 x SU(2), (alpha, A)(theta, y) = (theta + alpha, A(theta )y) is reducible - that is, A((.)) = B((.) + alpha )A(0)B((.))(-1), for some A(0) epsilon SU(2), B epsilon C-infinity(T-1,SU(2)),- is dense for the C-infinity-topology.
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作者：Epstein, CL
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作者：Schwartz, RE
摘要：We prove the Goldman-Parker Conjecture: A complex hyperbolic ideal triangle group is discretely embedded in PU(2, 1) if and only if the product of its three standard generators is not elliptic. We also prove that such a group is indiscrete if the product of its three standard generators is elliptic. A novel feature of this paper is that it uses a rigorous computer assisted proof to deal with difficult geometric estimates.
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作者：Lewis, J; Zagier, D
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作者：Adem, A; Smith, JH
摘要：In this paper we show that the cohomology of a connected CW-complex is periodic if and only if it is the base space of a spherical fibration with total space that is homotopically finite dimensional. As applications we characterize those discrete groups that act freely and properly on R-n x S-m; we construct nonstandard free actions of rank-two simple groups on finite complexes Y similar or equal to S-n x S-m; and we prove that a finite p-group P acts freely on such a complex if and only if it...
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作者：Zhang, SW
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作者：Ecker, K
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作者：Luo, WZ
摘要：This work is concerned with the validity of Weyl law for hyperbolic surfaces on the asymptotic counting of the Laplace eigenvalues. Following Phillips-Sarnak, we show that Weyl law is false for generic hyperbolic surfaces under the standard multiplicity assumption by establishing that a positive proportion of certain critical values of Rankin-Selberg L-functions do not vanish.
