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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.
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作者：Nekrashevych, Volodymyr
摘要：We describe a new class of groups of Burnside type, by giving a procedure transforming an arbitrary non-free minimal action of the dihedral group on a Cantor set into an orbit-equivalent action of an infinite finitely generated periodic group. We show that if the associated Schreier graphs are linearly repetitive, then the group is of intermediate growth. In particular, this gives first examples of simple groups of intermediate growth.
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作者：Isett, Philip
摘要：For any alpha < 1/3, we construct weak solutions to the 3D incompressible Euler equations in the class CtCx alpha that have nonempty, compact support in time on R x T-3 and therefore fail to conserve the total kinetic energy. This result, together with the proof of energy conservation for alpha > 1/3 due to [Eyink] and [Constantin, E, Titi], solves Onsager's conjecture that the exponent alpha = 1/3 marks the threshold for conservation of energy for weak solutions in the class (LtCx alpha)-C-in...
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作者：Bamler, Richard H.
摘要：In this paper we prove convergence and compactness results for Ricci flows with bounded scalar curvature and entropy. More specifically, we show that Ricci flows with bounded scalar curvature converge smoothly away from a singular set of codimension >= 4. We also establish a general form of the Hamilton-Tian Conjecture, which is even true in the Riemannian case. These results are based on a compactness theorem for Ricci flows with bounded scalar curvature, which states that any sequence of suc...
