On The Singular Set Of Harmonic Maps Into Dm Complexes
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On the Singular Set of Harmonic Maps into DM-Complexes
Author: Georgios Daskalopoulos
language: en
Publisher: American Mathematical Soc.
Release Date: 2016-01-25
The authors prove that the singular set of a harmonic map from a smooth Riemammian domain to a Riemannian DM-complex is of Hausdorff codimension at least two. They also explore monotonicity formulas and an order gap theorem for approximately harmonic maps. These regularity results have applications to rigidity problems examined in subsequent articles.
On Dwork's $p$-Adic Formal Congruences Theorem and Hypergeometric Mirror Maps
Author: E. Delaygue
language: en
Publisher: American Mathematical Soc.
Release Date: 2017-02-20
Using Dwork's theory, the authors prove a broad generalization of his famous -adic formal congruences theorem. This enables them to prove certain -adic congruences for the generalized hypergeometric series with rational parameters; in particular, they hold for any prime number and not only for almost all primes. Furthermore, using Christol's functions, the authors provide an explicit formula for the “Eisenstein constant” of any hypergeometric series with rational parameters. As an application of these results, the authors obtain an arithmetic statement “on average” of a new type concerning the integrality of Taylor coefficients of the associated mirror maps. It contains all the similar univariate integrality results in the literature, with the exception of certain refinements that hold only in very particular cases.
Nil Bohr-Sets and Almost Automorphy of Higher Order
Author: Wen Huang
language: en
Publisher: American Mathematical Soc.
Release Date: 2016-04-26
Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any d∈N does the collection of {n∈Z:S∩(S−n)∩…∩(S−dn)≠∅} with S syndetic coincide with that of Nild Bohr0 -sets? In the second part, the notion of d -step almost automorphic systems with d∈N∪{∞} is introduced and investigated, which is the generalization of the classical almost automorphic ones.