共查询到20条相似文献,搜索用时 31 毫秒
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Anton Alekseev Nariya Kawazumi Yusuke Kuno Florian Naef 《Comptes Rendus Mathematique》2017,355(2):123-127
We define a family of Kashiwara–Vergne problems associated with compact connected oriented 2-manifolds of genus g with boundary components. The problem is the classical Kashiwara–Vergne problem from Lie theory. We show the existence of solutions to for arbitrary g and n. The key point is the solution to based on the results by B. Enriquez on elliptic associators. Our construction is motivated by applications to the formality problem for the Goldman–Turaev Lie bialgebra . In more detail, we show that every solution to induces a Lie bialgebra isomorphism between and its associated graded . For , a similar result was obtained by G. Massuyeau using the Kontsevich integral. For , , our results imply that the obstruction to surjectivity of the Johnson homomorphism provided by the Turaev cobracket is equivalent to the Enomoto–Satoh obstruction. 相似文献
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For every real numbers , with , the curve parametrized by valued in with components: has image contained in the CR-umbilical locus: of the ellipsoid of equation , where the CR-umbilical locus of a Levi nondegenerate hypersurface is the set of points at which the Cartan curvature of M vanishes. 相似文献
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This paper deals with the following nonlinear elliptic equation where , is a bounded non-negative function in . By combining a finite reduction argument and local Pohozaev type of identities, we prove that if and has a stable critical point with and , then the above problem has infinitely many solutions. This paper overcomes the difficulty appearing in using the standard reduction method to locate the concentrating points of the solutions. 相似文献
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Sophie Grivaux 《Comptes Rendus Mathematique》2010,348(3-4):155-159
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Let q be a positive integer. Recently, Niu and Liu proved that, if , then the product is not a powerful number. In this note, we prove (1) that, for any odd prime power ? and , the product is not a powerful number, and (2) that, for any positive odd integer ?, there exists an integer such that, for any positive integer , the product is not a powerful number. 相似文献
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Let P be a set of n points in . The 2-center problem for P is to find two congruent balls of minimum radius whose union covers P. We present a randomized algorithm for computing a 2-center of P that runs in expected time; here , is the radius of the 2-center balls of P, and is the radius of the smallest enclosing ball of P. The algorithm is near quadratic as long as is not too close to , which is equivalent to the condition that the centers of the two covering balls be not too close to each other. This improves an earlier slightly super-cubic algorithm of Agarwal, Efrat, and Sharir (2000) [2] (at the cost of making the algorithm performance depend on the center separation of the covering balls). 相似文献
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