6 S ep 2 00 7 Quasisymmetric structures on surfaces ∗

Quasisymmetric structures on surfaces

We show that a locally Ahlfors 2-regular and locally linearly locally contractible metric surface is locally quasisymmetrically equivalent to the disk. We also discuss an application of this result to the problem of characterizing surfaces embedded in some Euclidean space that are locally bi-Lipschitz equivalent to a ball in the plane. In memoriam: Juha Heinonen (1960 2007)

ar X iv : 0 80 7 . 37 08 v 2 [ m at h . A G ] 4 S ep 2 00 8 K 3 surfaces with non - symplectic automorphisms of 2 - power order

This paper concerns complex algebraic K3 surfaces with an automorphism which acts trivially on the Néron-Severi group. Complementing a result by Vorontsov and Kondō, we determine those K3 surfaces where the order of the automorphism is a 2-power and equals the rank of the transcendental lattice. We also study the arithmetic of these K3 surfaces and comment on mirror symmetry.

ar X iv : h ep - p h / 06 09 07 7 v 1 7 S ep 2 00 6 Hadron multiplicities in e + e − annihilation with heavy primary quarks

ar X iv : h ep - t h / 03 12 06 2 v 2 7 D ec 2 00 3 More Membrane Matrix Model Solutions , – and Minimal Surfaces in S 7 Joakim

New solutions to the classical equations of motion of a bosonic matrix-membrane are given. Their continuum limit defines 3-manifolds (in Minkowski space) whose mean curvature vanishes. Part of the construction are minimal surfaces in S, and their discrete analogues. Some time ago [1], solutions of the bosonic matrix-model equations, .. Xi = − d ∑ j=1 [ [ Xi, Xj ] , Xj ]

ar X iv : m at h / 06 09 24 9 v 1 [ m at h . C O ] 8 S ep 2 00 6 P - PARTITION PRODUCTS AND FUNDAMENTAL QUASI - SYMMETRIC FUNCTION POSITIVITY

We show that certain differences of products of P-partition generating functions are positive in the basis of fundamental quasi-symmetric functions Lα. This result interpolates between recent Schur positivity and monomial positivity results of the same flavor. We study the case of chains in detail, introducing certain " cell transfer " operations on compositions and an interesting related " L-p...