Related papers: Height functions associated with closed subschemes
This note is an invitation to the theory of geometric functions. The foundation techniques and some of the developments in the field are explained with the mindset that the audience is principally young researchers wishing to understand…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a general method for introducing auxiliary polynomials to…
This paper presents a selected tour through the theory and applications of lifts of convex sets. A lift of a convex set is a higher-dimensional convex set that projects onto the original set. Many convex sets have lifts that are…
This paper is a survey of uniqueness results for stochastic differential equations with jumps and regularity results for the corresponding harmonic functions.
The aim of this article is to provide characterizations for subadditivity-like growth conditions for the so-called associated weight functions in terms of the defning weight sequence. Such growth requirements arise frequently in the…
A theory of sections of simplicial height functions is developed. At the core of this theory lies the section complex, which is assembled from higher section spaces. The latter encode flow lines along the height, as well as their…
We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and…
Robins et al, 2008, published a theory of higher order influence functions for inference in semi- and non-parametric models. This paper is a comprehensive manuscript from which Robins et al, was drawn. The current paper includes many…
The note complements topological aspects of the theory of chiral algebras.
A direct proof of Oka's lemma on the relation of holomorphic convexity and the properties of the distance to the boundary function is provided. Some related problems for subharmonicity properties of this function are also studied. A new…
In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalities on manifolds with non-convex boundary.
A fairly non-technical introduction to and survey of supersymmetry phenomenology with pedagogical emphasis, including exercises. Suitable for both theorists and experimentalists. The manuscript appeared as a Springer-Verlag monograph in…
In this paper, we consider the simultaneous approximation of real points by rational points with the error of approximation given by the functions of `non-standard' heights. We prove analogues of Khintchine and Jarn\'ik-Besicovitch theorems…
We present an explicit expression for the normalized height of a projective toric variety. This expression decomposes as a sum of local contributions, each term being the integral of a certain function, concave and piecewise linear-affine.…
A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it…
The Reeb space of a continuous function is the space of connected components of the level sets. In this paper we characterize those smooth functions on closed manifolds whose Reeb spaces have the structure of a finite graph. We also give…
In this paper, we give a height estimate for constant mean curvature graphs. Using this result we prove two results of uniqueness for the Dirichlet problem associated to the constant mean curvature equation on unbounded domains.
We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…
In this short note, we derive an upper-bound for the sum of two comparison functions, namely for the sum of a class K and an extended class K function. To the best of our knowledge, the relations derived in this note have not been…