TAILIEUCHUNG - Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks "

This paper is the first in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed Riemannian 3-manifold. The key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in R3 (with the flat metric). This study is undertaken here and completed in [CM6]. These local results are then applied in [CM7] where we describe the general structure of fixed genus surfaces in 3-manifolds. There are two local models for. | Annals of Mathematics The space of embedded minimal surfaces of fixed genus in a 3-manifold I Estimates off the axis for disks By Tobias H. Colding and William P. Minicozzi II Annals of Mathematics 160 2004 27 68 The space of embedded minimal surfaces of fixed genus in a 3-manifold I Estimates off the axis for disks By Tobias H. Colding and William P. Minicozzi II 0. Introduction This paper is the first in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed but arbitrary closed Riemannian 3-manifold. The key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in R3 with the flat metric . This study is undertaken here and completed in CM6 . These local results are then applied in CM7 where we describe the general structure of fixed genus surfaces in 3-manifolds. There are two local models for embedded minimal disks by an embedded disk we mean a smooth injective map from the closed unit ball in R2 into R3 . One model is the plane or more generally a minimal graph the other is a piece of a helicoid. In the first four papers of this series we will show that every embedded minimal disk is either a graph of a function or is a double spiral staircase where each staircase is a multi-valued graph. This will be done by showing that if the curvature is large at some point and hence the surface is not a graph then it is a double spiral staircase. To prove that such a disk is a double spiral staircase we will first prove that it is built out of N-valued graphs where N is a fixed number. This is initiated here and will be completed in the second paper. The third and fourth papers of this series will deal with how the multi-valued graphs fit together and in particular prove regularity of the set of points of large curvature - the axis of the double spiral staircase. The reader may find it useful to also look at the survey CM8 and the .

• Thạc sĩ - Tiến sĩ - Cao học
• embedded minimal
• subjects of mathematics
• Annals of Mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• simply connected
• Research methods
• Data collection methods
• Understanding scientific research
• Ensuring research validity
• Measurement techniques
• Sampling methods
• Scientific research capacity
• Educational institutions
• Policy and management studies
• Vietnam Academy for Ethnic minorities
• Scientific bases
• earth sciences
• Research
• VNU Journal of Science
• scientific reports
• Action research
• linguistics
• research projects
• Foreign Languages
• cooperative research
• Renewable energy
• Introduction to research
• Scientific investigation
• Scientific investigation research
• Experimental designs
• Measurement of variables
• Reading research
• Conducting and reading research
• Research process
• Research report
• Purpose of research
• Scientific method
• Conducting research
• The effect of university autonomy on training and scientific research
• Vietnam national university of agriculture
• Training and scientific research
• Vascular plant
• Flora
• Yen Tu
• Quang Ninh Research Forest
• statements and documents scientific reports
• medical reports
• medical knowledge
• medical research
• clinical trials
• medical management
• health care
• Methods in behavioral research
• Behavioral research
• Scientific understanding
• Fundamental research issues
• Measurement concepts
• Observational methods
• reading comprehension
• education
• optimal picket
• model creation
• urban expansion
• organizing spatial
• Journal of Science
• Journal of Technology
• Technology Management
• Research quality
• Strategy and policy
• Summary of Doctoral thesis
• Summary of Doctoral thesis in public Management
• State management
• Female scientific research human
• Research human resource development
• Scientific research and teaching
• Defense and security education
• Current situation and solutions
• Security education
• Structural biochemistry
• epigenetics
• MicroRNAs
• Tạp chí khoa học
• Tạp chí Công nghệ
• Quản lý công nghệ
• Human resources
• Science management
• Poliomyelitis vaccine Research
• Non Ri Maprec
• Production center