Related papers: Application of integral geometry to minimal surfac…

This note corrects an erroneous statement in Lemma 3.8 of the author's paper Embedded Contact Homology and Seiberg-Witten Floer Homology IV which was published in Volume 14 of Geometry and Topology in 2009.

In this article, we consider a modified version of minimal $L^2$ integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points, and obtain a concavity property of the modified version. As an application, we…

The paper suggests a short survey of integration algorithms which evolved since 1982. These theorems and algorithms form discrete versions of the calculus theorems.

In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.

This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.

In this paper, we generalise an interesting geometry problem from the 1995 edition of the International Mathematical Olympiad (IMO) using analytic geometry tools.

The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…

We give a brief survey of some of the geometry of mirror symmetry, written in 2004 for the "Encyclopaedia of Mathematical Physics". Probably a little bit out of date now in a few places, but hey.

We give an overview of results on irregular complex surfaces of general type, discussing in particular the distribution of the numerical invariants self-intersection of a canonical divisor and holomorphic Euler characteristic for the…

A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.

Minimal surfaces are among the most natural objects in Differential Geometry, and have been studied for the past 250 years ever since the pioneering work of Lagrange. The subject is characterized by a profound beauty, but perhaps even more…

This note is a survey of the enumerative geometry of rational curves on Calabi-Yau threefolds, based on a talk given by the author at the May 1991 Workshop on Mirror Symmetry at MSRI. An earlier version appeared in "Essays on Mirror…

We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any explicit parameterization and is…

This paper has been withdrawn, because its material has been revised and became part of paper math.GT/0010184

Geometrical structures intrinsic to non-expanding, weakly isolated and isolated horizons are analyzed and compared with structures which arise in other contexts within general relativity, e.g., at null infinity. In particular, we address in…

An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.

These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…

We give a brief introduction to some of the recent works on finding geometric structures on triangulated surfaces using variational principles.

We present a result on topologically equivalent integral metrics (Rachev, 1991, Muller, 1997) that metrize weak convergence of laws with common marginals. This result is relevant for applications, as shown in a few simple examples.

In this article, we study the ramification of the Gauss map of complete minimal surfaces in R^m on annular ends. This work is a continuation of previous work of Dethloff-Ha. We thus give an improvement of the results on annular ends of…