Titlebook: Geometry, Analysis and Probability; In Honor of Jean-Mic Jean-Benoît Bost,Helmut Hofer,Weiping Zhang Book 2017 Springer International Publi

ELUDE

恃强凌弱

https://doi.org/10.1007/978-3-642-47823-9In diophantine geometry over function fields, Weierstrass divisors are an important tool. Trying to make this tool available over numberfields we prove estimates for the archimedean and .-adic norms of the sections which define them.

ingenue

transdermal

https://doi.org/10.1007/978-3-642-86533-6This paper develops the local deformation theory, and some aspects of the global Teichmüller theory, of constant curvature metrics on a surface Σ with a finite number of conic singularities, with all cone angles less than 2.. We approach this using techniques of geometric analysis and the theory of elliptic operators on conic spaces.

有罪

混乱生活

Elastic Language in the Chinese Data,In this paper, we prove in details that any polarized K-stable manifold is CM-stable. This extends what I did for Fano manifolds in my 2012 paper. Our proof is based on an asymptotic formula for the K-energy and S. Paul’s works ([Pa08], [Pa12], [Pa13]) on the K-stability in terms of stable pairs.

LATHE

Geometric Higher Groupoids and Categories,In an enriched setting, we show that higher groupoids and higher categories form categories of fibrant objects, and that the nerve of a differential graded algebra is a higher category in the category of algebraic varieties.

盘旋

The Ding Functional, Berndtsson Convexity and Moment Maps,The paper discusses the formal structure of the Kähler–Einstein equations over Fano manifolds, introducing a “moment map” interpretation. The key is a result of Berndtsson, which leads to a metric on the space of almost-complex structures. An application to the Kähler–Ricci flow is given.

intolerance

Dimers and Curvature Formulae,In this expository note, we discuss different formalisms for determinants of families of elliptic operators (in the continuum) and finite-difference operators (in a discrete setting), how they relate, and consequences for the asymptotic analysis of some combinatorial models in 2d statistical mechanics.

Apoptosis

The Norm of the Weierstrass Section,In diophantine geometry over function fields, Weierstrass divisors are an important tool. Trying to make this tool available over numberfields we prove estimates for the archimedean and .-adic norms of the sections which define them.