-
作者：Barlow, Martin T.; Murugan, Mathav
摘要：We prove that the elliptic Harnack inequality (on a manifold, graph, or suitably regular metric measure space) is stable under bounded perturbations, as well as rough isometrics.
-
作者：Yuan, Xinyi; Zhang, Shou-Wu
摘要：The Colmez conjecture is a formula expressing the Faltings height of an abelian variety with complex multiplication in terms of some linear combination of logarithmic derivatives of Artin L-functions. The aim of this paper to prove an averaged version of the conjecture, which was also proposed by Colmez.
-
作者：Logunov, Alexander
摘要：Let M be a compact C-infinity-smooth Riemannian manifold of dimension n, n >= 3, and let phi lambda : Delta M phi lambda + lambda phi lambda = 0 denote the Laplace eigenfunction on M corresponding to the eigenvalue lambda. We show that Hn-1 ({phi lambda = 0}) <= C lambda(alpha), where alpha > 1/2 is a constant, which depends on n only, and C > 0 depends on M. This result is a consequence of our study of zero sets of harmonic functions on C-infinity-smooth Riemannian manifolds. We develop a tec...
-
作者：Bresch, Didier; Jabin, Pierre-emmanuel
摘要：We prove global existence of appropriate weak solutions for the compressible Navier-Stokes equations for a more general stress tensor than those previously covered by P.-L.Lions and E. Feireisl's theory. More precisely we focus on more general pressure laws that are not thermodynamically stable; we are also able to handle some anisotropy in the viscous stress tensor. To give answers to these two longstanding problems, we revisit the classical compactness theory on the density by obtaining prec...
-
作者：Gan, Wee Teck; Ichino, Atsushi
摘要：We generalize the Shimura-Waldspurger correspondence, which describes the generic part of the automorphic discrete spectrum of the metaplectic group Mp(2), to the metaplectic group Mp(2n) of higher rank. To establish this, we transport Arthur's endoscopic classification of representations of the odd special orthogonal group SO2r+1 with r >> 2n by using a result of J.-S. Li on global theta lifts in the stable range.
-
作者：Georgieva, Penka; Zinger, Aleksey
摘要：We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the renowned quintic threefold. In some cases, our invariants provide lower bounds for counts of real positive-genus curves in real algebraic varieties. Our approach to the orientability problem is based entirely on the topology of real bundle pairs over symmetric surfaces; the previous attempts involved direct computations for the determinan...
-
作者：Evseev, Anton; Kleshchev, Alexander
摘要：We prove Turner's conjecture, which describes the blocks of the Hecke algebras of the symmetric groups up to derived equivalence as certain explicit Turner double algebras. Turner doubles are Schur-algebra-like 'local' objects, which replace wreath products of Brauer tree algebras in the context of the Broue abelian defect group conjecture for blocks of symmetric groups with non-abelian defect groups. The main tools used in the proof are generalized Schur algebras corresponding to wreath produ...
-
作者：Mirkovic, I.; Vilonen, K.
-
作者：Eskin, Alex; Filip, Simion; Wright, Alex
摘要：We compute the algebraic hull of the Kontsevich Zorich cocycle over any GL(2)(+) (R) invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarieties.
-
作者：Liokumovich, Yevgeny; Marques, Fernando C.; Neves, Andre
摘要：Given M a Riemannian manifold with (possibly empty) boundary, we show that its volume spectrum {omega(Rho)(M)}(p is an element of N) satisfies a Weyl law that was conjectured by Gromov.
