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作者：Moreira, Carlos Gustavo T. de A.; Zamudio, Alex Mauricio
摘要：This is an erratum for the paper Stable intersections of regular Cantor sets with large Hausdorff dimensions by Moreira and Yoccoz. We show how to fix a flaw - a bad choice of parameters - in the proof of the scale recurrence lemma. This lemma is an important step towards establishing the main theorem.
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作者：Brown, Aaron; Fisher, David; Hurtado, Sebastian
摘要：We prove several cases of Zimmer's conjecture for actions of higher-rank, cocompact lattices on low-dimensional manifolds. For example, if 1-' is a cocompact lattice in SL(n, R), M is a compact manifold, and omega a volume form on M, we show that any homomorphism alpha: 1-'-+ Diff(M) has finite image if the dimension of M is less than n - 1 and that any homomor-phism alpha: 1-'-+ Diff(M, omega) has finite image if the dimension of M is less than n. The key step in the proof is to show that any...
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作者：Merle, Frank; Raphael, Pierre; Rodnianski, Igor; Szeftel, Jeremie
摘要：In this paper, which continues our investigation of strong singularity formation in compressible fluids, we consider the compressible three-dimensional Navier-Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations implode (with infinite density) at a later time at a point, and completely describe the associated formation of singularity. An essential step in the proof is...
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作者：Krause, Ben; Mirek, Mariusz; Tao, Terence
摘要：We establish convergence in norm and pointwise almost everywhere for the non-conventional (in the sense of Furstenberg) bilinear polynomial ergodic averages AN(f,g)(x) := 1/N Sigma(N)(n=1) f(T(n)x)g(T(P(n))x) as N -> infinity, where T: X -> X is a measure-preserving transformation of a sigma-finite measure space (X, mu), P(n) is an element of Z[n] is a polynomial of degree d >= 2, and f is an element of L-P1 (X), g is an element of L-P2 (X) for some p1 ,p 2 > 1 with 1/p1 + 1/p2 <= 1. We also e...
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作者：Cohn, Henry; Kumar, Abhinav; Miller, Stephen D.; Radchenko, Danylo; Viazovska, Maryna
摘要：We prove that the E8 root lattice and the Leech lattice are universally optimal among point configurations in Euclidean spaces of dimensions eight and twenty-four, respectively. In other words, they minimize energy for every potential function that is a completely monotonic function of squared distance (for example, inverse power laws or Gaussians), which is a strong form of robustness not previously known for any configuration in more than one dimension. This theorem implies their recently sh...
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作者：Hausmann, Markus
摘要：For every abelian compact Lie group A, we prove that the homotopical A-equivariant complex bordism ring, introduced by tom Dieck (1970), is isomorphic to the A-equivariant Lazard ring, introduced by Cole-Greenlees-Kriz (2000). This settles a conjecture of Greenlees. We also show an analog for homotopical real bordism rings over elementary abelian 2-groups. Our results generalize classical theorems of Quillen (1969) on the connection between non-equivariant bordism rings and formal group laws, ...
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作者：Milman, Emanuel; Neeman, Joe
摘要：We establish the Gaussian Multi-Bubble Conjecture: the least Gaussianweighted perimeter way to decompose Rn into q cells of prescribed (positive) Gaussian measure when 2 < q < n+ 1, is to use a simplicial cluster, obtained from the Voronoi cells of q equidistant points. Moreover, we prove that simplicial clusters are the unique isoperimetric minimizers (up to nullsets). In particular, the case q = 3 confirms the Gaussian Double-Bubble Conjecture: the unique least Gaussian-weighted perimeter wa...
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作者：Bachmann, Tom; Kong, Hana Jia; Wang, Guozhen; Xu, Zhouli
摘要：We define the Chow t-structure on the infinity-category of motivic spectra SH(k) over an arbitrary base field k. We identify the heart of this t-structure SH(k)(c(sic)) when the exponential characteristic of k is inverted. Restricting to the cellular subcategory, we identify the Chow heart SH(k)(cell,c(sic)) as the category of even graded MU2*MU-comodules. Furthermore, we show that the co-category of modules over the Chow truncated sphere spectrum 1(c=0) is algebraic. Our results generalize th...
