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作者：Okikiolu, K
摘要：Let M be a closed compact n-dimensional manifold with n odd. We calculate the first and second variations of the zeta-regularized determinants det ' Delta and det L as the metric on M varies, where Delta denotes the Laplacian on functions and L denotes the conformal Laplacian. We see that the behavior of these functionals depends on the dimension. Indeed, every critical metric for (-1)((n-1)/2)det ' Delta or (-1)((n-1)/2)\det L\ has finite index. Consequently there are no local maxima if n = 4...
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作者：Szabó, ZI
摘要：The first isospectral pairs of metrics are constructed on the most simple simply connected domains, namely, on balls and spheres. This long-standing problem, concerning the existence of such pairs, has been solved by a new method called anticommutator technique. Among the wide range of such pairs, the most striking examples are provided on the spheres S4k-1, where k greater than or equal to 3. One of these metrics is homogeneous (since it is the metric on the geodesic sphere of a 2-point homog...
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作者：Kashiwabara, T
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作者：Brudnyi, A
摘要：We estimate the expected number of limit cycles of a planar polynomial vector field situated in a neighbourhood of the origin provided that the field in a larger neighbourhood is close enough to a linear center. Our main tool is a distributional inequality for the number of zeros of some families of univariate holomorphic functions depending analytically on a parameter. We obtain this inequality by methods of pluripotential theory. This inequality also implies versions of a strong law of large...
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作者：Moreira, CGTD; Yoccoz, JC
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作者：Emerton, M; Kisin, M
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作者：Thunder, JL
摘要：We consider Diophantine inequalities of the kind /F(x)/ less than or equal to m, where F(X) is an element of Z[X] is a homogeneous polynomial which can be expressed as a product of d homogeneous linear forms in n variables with complex coefficients and m greater than or equal to 1. We say such a form is of finite type if the total volume of all real solutions to this inequality is finite and if, for every n ' -dimensional subspace S subset of or equal to R-n defined over Q, the corresponding n...
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作者：van den Berg, M; Bolthausen, E; den Hollander, F
摘要：For a > 0, let W-a(t) be the a-neighbourhood of standard Brownian motion in R-d starting at 0 and observed until time t. It is well-known that E\W-a(t)\ similar to kappa (a)t (t --> infinity) for d greater than or equal to 3, with kappa (a) the Newtonian capacity of the ball with radius a. We prove that lim(t --> infinity) 1/t((d-2))/d log P(\W-a(t)\ less than or equal to bt) = -I-kappaa (b) is an element of (-infinity ,0) for all 0 < b < kappa (a) and derive a variational representation for t...
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作者：Darmon, H
摘要：This article describes a conjectural p-adic analytic construction of global points on (modular) elliptic curves, points which are defined over the ring class fields of real quadratic fields. The resulting conjectures suggest that the classical Heegner point construction, and the theory of complex multiplication on which it is based, should extend to a variety of contexts in which the underlying field is not a CM field.
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作者：Oort, F
