Author: Hirotaka FujimotoPublisher:
ISBN:
Category :
Languages : en
Pages : 31
Book Description
Value distribution of the Gauss map of complete minimal surfaces in IRm
Author: Hirotaka FujimotoValue Distribution Theory of the Gauss Map of Minimal Surfaces in Rm
Author: Hirotaka FujimotoPublisher: Springer Science & Business Media
ISBN: 332280271X
Category : Mathematics
Languages : en
Pages : 222
Book Description
This book presents in a systematic and almost self-contained way the striking analogy between classical function theory, in particular the value distribution theory of holomorphic curves in projective space, on the one hand, and important and beautiful properties of the Gauss map of minimal surfaces on the other hand. Both theories are developed in the text, including many results of recent research. The relations and analogies between them become completely clear. The book is written for interested graduate students and mathematicians, who want to become more familiar with this modern development in the two classical areas of mathematics, but also for those, who intend to do further research on minimal surfaces.
Value Distribution of the Gauss Maps of Complete Minimal Surfaces in R
Author: H. FujimotoThe Geometry of the Generalized Gauss Map
Author: David A. HoffmanPublisher: American Mathematical Soc.
ISBN: 0821822365
Category : Mathematics
Languages : en
Pages : 113
Book Description
This paper is devoted primarily to the study of properties of the Grassmannian of oriented 2-planes in [double-struck capital]R[superscript]n and to applications of these properties to understanding minimal surfaces in [double-struck capital]R[superscript]n via the generalized Gauss map. The extrinsic geometry of the Grassmannian, when considered as a submanifold of [double-struck capital]CP[superscript]n-2, is investigated, with special emphasis on the nature of the intersection of the Grassmannian with linear subspaces of [double-struck capital]CP[superscript]n-1. These results are the basis for a discussion of minimal surfaces that are degenerate in various ways; understanding the different types of degeneracy and their interrelations is a critical step toward obtaining a clear picture of the basic geometric properties of minimal surfaces in [double-struck capital]R[superscript]n.
On Values of Gauss Maps of Complete Minimal Surfaces on Annular Ends
Author: Shu-Jung KaoPublisher:
ISBN:
Category : Gauss maps
Languages : en
Pages : 13
Book Description
Gauss Maps and Moduli Spaces of Minimal Surfaces in Euclidean Spaces
Author: Xiaokang MoOn the Gauss Map of Complete Minimal Surfaces with Finite Total Curvature
Author: Yi FangOn the Gauss map of a complete minimal surface in ... [Rm]
![On the Gauss map of a complete minimal surface in ... [Rm] PDF](https://books.google.com/books/content/images/frontcover/ktTktgAACAAJ?fife=w80-h100)
Author: Hirotaka FujimotoOn the Gauss Map of Minimal Surfaces Immersed in $R N$
Author: Min RuGrassmannians and Gauss Maps in Piecewise-Linear Topology
Author: Norman LevittPublisher: Springer
ISBN: 3540460780
Category : Mathematics
Languages : en
Pages : 208
Book Description
The book explores the possibility of extending the notions of "Grassmannian" and "Gauss map" to the PL category. They are distinguished from "classifying space" and "classifying map" which are essentially homotopy-theoretic notions. The analogs of Grassmannian and Gauss map defined incorporate geometric and combinatorial information. Principal applications involve characteristic class theory, smoothing theory, and the existence of immersion satifying certain geometric criteria, e.g. curvature conditions. The book assumes knowledge of basic differential topology and bundle theory, including Hirsch-Gromov-Phillips theory, as well as the analogous theories for the PL category. The work should be of interest to mathematicians concerned with geometric topology, PL and PD aspects of differential geometry and the geometry of polyhedra.