Bellman Function For Extremal Problems In Bmo Ii Evolution
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Bellman Function for Extremal Problems in BMO II: Evolution
Author: Paata Ivanisvili
language: en
Publisher: American Mathematical Soc.
Release Date: 2018-10-03
In a previous study, the authors built the Bellman function for integral functionals on the space. The present paper provides a development of the subject. They abandon the majority of unwanted restrictions on the function that generates the functional. It is the new evolutional approach that allows the authors to treat the problem in its natural setting. What is more, these new considerations lighten dynamical aspects of the Bellman function, in particular, the evolution of its picture.
The Bellman Function Technique in Harmonic Analysis
Author: Vasily Vasyunin
language: en
Publisher: Cambridge University Press
Release Date: 2020-08-06
A comprehensive reference on the Bellman function method and its applications to various topics in probability and harmonic analysis.
Flat Rank Two Vector Bundles on Genus Two Curves
Author: Viktoria Heu
language: en
Publisher: American Mathematical Soc.
Release Date: 2019-06-10
The authors study the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of underlying vector bundles (including unstable bundles), for which they compute a natural Lagrangian rational section. As a particularity of the genus case, connections as above are invariant under the hyperelliptic involution: they descend as rank logarithmic connections over the Riemann sphere. The authors establish explicit links between the well-known moduli space of the underlying parabolic bundles with the classical approaches by Narasimhan-Ramanan, Tyurin and Bertram. This allows the authors to explain a certain number of geometric phenomena in the considered moduli spaces such as the classical -configuration of the Kummer surface. The authors also recover a Poincaré family due to Bolognesi on a degree 2 cover of the Narasimhan-Ramanan moduli space. They explicitly compute the Hitchin integrable system on the moduli space of Higgs bundles and compare the Hitchin Hamiltonians with those found by van Geemen-Previato. They explicitly describe the isomonodromic foliation in the moduli space of vector bundles with -connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles.