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Satyanad Kichenassamy 《Advances in Mathematics》2004,184(2):268-288
In 1985, Fefferman and Graham have constructed a local embedding of an arbitrary real-analytic manifold, of odd dimension n, into a Ricci-flat manifold of dimension n+2 admitting a homothety. They conjectured that their result remains valid in even dimensions, if logarithms are allowed in the expansion of the metric. In this paper, we (i) prove that such expansions exist and converge and (ii) establish the degree of non-uniqueness of the solution in terms of the coefficients in the expansion. 相似文献
26.
Dmitri I. Panyushev 《Advances in Mathematics》2004,186(2):307-316
We study Abelian ideals of a Borel subalgebra consisting of long roots. It is shown that methods of Cellini and Papi can be extended to this situation. A uniform expression for the number of long Abelian ideals is given. We also show that there is a one-to-one correspondence between the long Abelian ideals and B-stable commutative subalgebras in the little adjoint representation of the Langlands dual Lie algebra. 相似文献
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The formation of thinning filaments is commonly observed previously to the break-up of a very viscous jet. This paper shows that a fluid under capillary forces cannot break-up through the uniform collapse of a filament. 相似文献
28.
Multilinear interpolation is a powerful tool used in obtaining strong-type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak Lq estimate for a single index q (which may be less than one) and that all the adjoints of the multilinear operator are of similar nature, and thus they also satisfy the same weak Lq estimate. Under this assumption, in this note we give a general multilinear interpolation theorem which allows one to obtain strong-type boundedness for the operator (and all of its adjoints) for a large set of exponents. The key point in the applications we discuss is that the interpolation theorem can handle the case q?1. When q>1, weak Lq has a predual, and such strong-type boundedness can be easily obtained by duality and multilinear interpolation (cf. Interpolation Spaces, An Introduction, Springer, New York, 1976; Math. Ann. 319 (2001) 151; in: Function Spaces and Applications (Lund, 1986), Lecture Notes in Mathematics, Vol. 1302, Springer, Berlin, New York, 1988; J. Amer. Math. Soc. 15 (2002) 469; Proc. Amer. Math. Soc. 21 (1969) 441). 相似文献
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Marco Biroli Silvia Mataloni Michele Matzeu 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(3):295-321
Some stability results for Mountain Pass and Linking type solutions of semilinear problems involving a very general class
of Dirichlet forms are stated. The non linear terms are supposed to have a suitable superlinear growth and the family of Dirichlet
forms is required to be dominated from below and from above by a fixed diffusion type form. Some concrete examples are also
given. 相似文献
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