1 - 10 of 18 articles
We study the quotient of the mapping class group Modgn of a surface of genus g with n punctures, by the subgroup Modgn[p] generated by the pth powers of Dehn twists.
In this note, we show that the bi‐invariant Einstein metric on the compact Lie group G2 is dynamically unstable as a fixed point of the Ricci flow. This completes the stability analysis for the bi‐invariant metrics on the compact, connected, simple Lie groups. Interestingly, G2 is the only...
For any lattice congruence of the weak order on Sn, N. Reading proved that glueing together the cones of the braid fan that belong to the same congruence class defines a complete fan. We prove that this fan is the normal fan of a polytope.
We show that if the second eigenvalue λ of a d‐regular graph G on n∈3Z vertices is at most εd2/(nlogn), for a small constant ε>0, then G contains a triangle‐factor. The bound on λ is at most an O(logn) factor away from the best possible one: Krivelevich, Sudakov and Szabó, extending a...
We give a modified, very natural definition for the complex Monge–Ampère operator for an ω‐plurisubharmonic (psh) function φ with analytic singularities on a Kähler manifold (X,ω) of dimension n which has the property ∫X(ω+ddcφ)n=∫Xωn if X is compact. This means that, unlike in the previous...
This note verifies a conjecture of Armitage and Goldstein that annular domains may be characterized as quadrature domains for harmonic functions with respect to a uniformly distributed measure on a sphere.
The set of totally geodesic representatives of a homotopy class of maps from a compact Riemannian manifold M with nonnegative Ricci curvature into a complete Riemannian manifold N with no focal points is path‐connected and, when nonempty, equal to the set of energy‐minimizing maps in that class....
We prove that a Hopf algebra of prime dimension p over an algebraically closed field, whose characteristic is equal to p, is either a group algebra or a restricted universal enveloping algebra. Moreover, we show that any Hopf algebra of prime dimension p over a field of characteristic q>0 is...
We show that any q‐multiplicative sequence which is oscillating of order 1, that is, does not correlate with linear phase functions e2πinα (α∈R), is Gowers uniform of all orders, and hence in particular does not correlate with polynomial phase functions e2πip(n) (p∈R[x]). Quantitatively, we show...
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