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作者：Ai, Albert; Ifrim, Mihaela; Tataru, Daniel
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
摘要：It has long been conjectured that for nonlinear wave equations that satisfy a nonlinear form of the null condition, the low regularity well-posedness theory can be significantly improved compared to the sharp results of Smith-Tataru for the generic case. The aim of this article is to prove the first result in this direction, namely for the time-like minimal surface equation in the Minkowski space-time. Further, our improvement is substantial, namely by 3/8 derivatives in two space dimensions a...
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作者：Kottke, Chris; Rochon, Frederic
作者单位：State University System of Florida; New College Florida; University of Quebec; University of Quebec Montreal
摘要：We develop new techniques to compute the weighted L-2-cohomology of quasi-fibered boundary metrics (QFB-metrics). Combined with the decay of L-2-harmonic forms obtained in a companion paper, this allows us to compute the reduced L-2-cohomology for various classes of QFB-metrics. Our results applies in particular to the Nakajima metric on the Hilbert scheme of n points on C-2 , for which we can show that the Vafa-Witten conjecture holds. Using the compactification of the monopole moduli space a...
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作者：Bera, Sayani; Verma, Kaushal
作者单位：Department of Science & Technology (India); Indian Association for the Cultivation of Science (IACS) - Jadavpur; Indian Institute of Science (IISC) - Bangalore
摘要：It has been conjectured that every stable manifold arising from a holomorphic automorphism, that acts hyperbolically on a compact invariant set, is biholomorphic to complex Euclidean space. Such stable manifolds are known to be biholomorphic to the basin of a uniformly attracting family of holomorphic maps. It is shown that the basin of a uniformly attracting family of holomorphic maps is biholomorphic to complex Euclidean space and this resolves the conjecture on the biholomorphism type of su...
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作者：Azagra, Daniel; Drake, Marjorie; Hajlasz, Piotr
作者单位：Complutense University of Madrid; Massachusetts Institute of Technology (MIT); Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We prove that if u : R-n -> R strongly convex, then for every epsilon>0 there is a strongly convex function v is an element of C-2(Rn) such that |{u not equal v}|
