Some geometric aspects of Puiseux surfaces

On the Moduli Space of Singular Euclidean Surfaces

The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces.

Geometric Modeling of Parallel Curves on Surfaces

This paper is concerned with various aspects of the modeling of parallel curves on surfaces with special emphasis on surfaces of revolution. An algorithm for efficient tracking of the geodesics on these surfaces is presented. Existing methods for plane offset curves are adapted to generate G-spline approximations of parallel curves on arbitrary surfaces. An algorithm to determine singularities ...

Survey on Geometric Iterative Methods with Applications

Geometric iterative method, also called progressive-iterative approximation (PIA), is an iterative method with clear geometric meaning. Just by adjusting the control points of curves or surfaces iteratively, the limit curve or surface will interpolate (approximate) the given data point set. In this paper, we introduce the geometric iterative method in two aspects, i.e., theory and application. ...

The Optimal Constant in Wente's L1 Estimate

We explore some geometric aspects of compensation compactness associated to Jacobian determinants. We provide the optimal constant in Wente's inequality-the original motivation of this work-and go on to give various extensions to geometric situations. In fact we improve Wente's inequality somewhat, making it more appropriate for applications in which optimal results are required. This is demons...

Geometric Aspects of the Moduli Spaces of Riemann Surfaces