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作者：HEINONEN, J; KOSKELA, P
摘要：We establish that the infinitesimal ''H-definition'' for quasiconformal mappings on Carnot groups implies global quasisymmetry, and hence the absolute continuity on almost all lines. Our method is new even in R(n) where we obtain that the ''limsup'' condition in the H-definition can be replaced by a ''liminf'' condition. This leads to a new removability result for (quasi)conformal mappings in Euclidean spaces. An application to parametrizations of chord-are surfaces is also given.
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作者：BOROVOI, M; RUDNICK, Z
作者单位：Princeton University
摘要：We are interested in counting integer and rational points in affine algebraic varieties, also under congruence conditions. We introduce the notions of a strongly Hardy-Littlewood variety and a relatively Hardy-Littlewood variety, in terms of counting rational points satisfying congruence conditions. The definition of a strongly Hardy-Littlewood variety is given in such a way that varieties for which the Hardy-Littlewood circle method is applicable are strongly Hardy-Littlewood. We prove that c...
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作者：PREMET, A
作者单位：University of California System; University of California Riverside
摘要：Let g be the Lie algebra of a connected reductive group G over an algebraically closed field of characteristic p > 0. Suppose that G((1)) is simply connected and p is good for the root system of G. If p = 2, suppose in addition that g admits a nondegenerate G-invariant trace form. Let V be an irreducible and faithful g-module with p-character chi is an element of g*. It is proved in the paper that dim V is divisible by p(1/2dim Omega(chi)) where Omega(chi) stands for the orbit of chi under the...
