TAILIEUCHUNG - Đề tài " The Calabi-Yau conjectures for embedded surfaces "

In this paper we will prove the Calabi-Yau conjectures for embedded surfaces (., surfaces without self-intersection). In fact, we will prove considerably more. The heart of our argument is very general and should apply to a variety of situations, as will be more apparent once we describe the main steps of the proof later in the introduction. | Annals of Mathematics The Calabi-Yau conjectures for embedded surfaces By Tobias H. Colding and William P. Minicozzi II Annals of Mathematics 167 2008 211-243 The Calabi-Yau conjectures for embedded surfaces By Tobias H. Colding and William P. Minicozzi II 0. Introduction In this paper we will prove the Calabi-Yau conjectures for embedded surfaces . surfaces without self-intersection . In fact we will prove considerably more. The heart of our argument is very general and should apply to a variety of situations as will be more apparent once we describe the main steps of the proof later in the introduction. The Calabi-Yau conjectures about surfaces date back to the 1960s. Much work has been done on them over the past four decades. In particular examples of Jorge-Xavier from 1980 and Nadirashvili from 1996 showed that the immersed versions were false we will show here that for embedded surfaces . injective immersions they are in fact true. Their original form was given in 1965 in Ca where E. Calabi made the following two conjectures about minimal surfaces they were also promoted by S. S. Chern at the same time see page 212 of Ch Conjecture . Prove that a complete minimal hypersurface in R must be unbounded. Calabi continued It is known that there are no compact minimal submanifolds of R or of any simply connected complete Riemannian manifold with sectional curvature 0 . A more ambitious conjecture is Conjecture . A complete nonflat minimal hypersurface in R has an unbounded projection in every n 2 -dimensional flat subspace. These conjectures were revisited in S. T. Yau s 1982 problem list see problem 91 in Ya1 by which time the Jorge-Xavier paper had appeared Question . Is there any complete minimal surface in R3 which is a subset of the unit ball The authors were partially supported by NSF Grants DMS-0104453 and DMS-0104187. 212 TOBIAS H. COLDING AND WILLIAM P. MINICOZZI II This was asked by Calabi Ca . There is an example of a complete nonflat .

• Thạc sĩ - Tiến sĩ - Cao học
• embedded surfaces
• subjects of mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• embedded minimal
• Annals of Mathematics
• tài liệu báo cáo nghiên cứu khoa học
• cách trình bày báo cáo
• kiến thức toán học
• báo cáo toán học
• công trình toán học
• simply connected
• báo cáo khoa học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• 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