On A Free Boundary Problem For Embedded Minimal Surfaces And Instability Theorems For Manifolds With Positive Isotropic Curvature
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On A Free Boundary Problem For Embedded Minimal Surfaces And Instability Theorems For Manifolds With Positive Isotropic Curvature
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Author : Man Chun Li
language : en
Publisher: Stanford University
Release Date : 2011
On A Free Boundary Problem For Embedded Minimal Surfaces And Instability Theorems For Manifolds With Positive Isotropic Curvature written by Man Chun Li and has been published by Stanford University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
In this thesis, we describe a min-max construction of embedded minimal surfaces satisfying the free boundary condition in any compact 3-manifolds with boundary. We also prove the instability of minimal surfaces of certain conformal type in 4- manifolds with positive isotropic curvature. Given a compact 3-manifold M with boundary [d̳]M, consider the problem of find- ing an embedded minimal surface [Sigma] which meets [d̳]M orthogonally along [d̳][Sigma]. These surfaces are critical points to the area functional with respect to variations preserving [delta]M. We will use a min-max construction to construct such a free boundary solution and prove the regularity of such solution up to the free boundary. An interesting point is that no convexity assumption on [d̳]M is required. We also discuss some geometric properties, genus bounds for example, for these free boundary solutions. Just as positive sectional curvature tends to make geodesics unstable, positive isotropic curvature tends to make minimal surfaces unstable. In the second part of this thesis, we prove a similar instability result in dimension 4. Given a compact 4- manifold M with positive isotropic curvature, we show that any complete immersed minimal surface [Sigma] in M which is uniformly conformally equivalent to the complex plane is unstable. The same conclusion holds in higher dimensions as well if we assume that the manifold has uniformly positive complex sectional curvature. The proof uses the H ̈ormander's weighted L^2 method and the stability inequality to derive a contradiction.
On A Free Boundary Problem For Embedded Minimal Surfaces And Instability Theorems For Manifolds With Positive Isotropic Curvature
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Author : Man Chun Li
language : en
Publisher:
Release Date : 2011
On A Free Boundary Problem For Embedded Minimal Surfaces And Instability Theorems For Manifolds With Positive Isotropic Curvature written by Man Chun Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
In this thesis, we describe a min-max construction of embedded minimal surfaces satisfying the free boundary condition in any compact 3-manifolds with boundary. We also prove the instability of minimal surfaces of certain conformal type in 4- manifolds with positive isotropic curvature. Given a compact 3-manifold M with boundary [d̳]M, consider the problem of find- ing an embedded minimal surface [Sigma] which meets [d̳]M orthogonally along [d̳][Sigma]. These surfaces are critical points to the area functional with respect to variations preserving [delta]M. We will use a min-max construction to construct such a free boundary solution and prove the regularity of such solution up to the free boundary. An interesting point is that no convexity assumption on [d̳]M is required. We also discuss some geometric properties, genus bounds for example, for these free boundary solutions. Just as positive sectional curvature tends to make geodesics unstable, positive isotropic curvature tends to make minimal surfaces unstable. In the second part of this thesis, we prove a similar instability result in dimension 4. Given a compact 4- manifold M with positive isotropic curvature, we show that any complete immersed minimal surface [Sigma] in M which is uniformly conformally equivalent to the complex plane is unstable. The same conclusion holds in higher dimensions as well if we assume that the manifold has uniformly positive complex sectional curvature. The proof uses the H ̈ormander's weighted L^2 method and the stability inequality to derive a contradiction.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 1987
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Free Boundary Problems In Continuum Mechanics
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Author : S.N. Antontsev
language : en
Publisher: Birkhäuser
Release Date : 2013-03-07
Free Boundary Problems In Continuum Mechanics written by S.N. Antontsev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Social Science categories.
Progress in different fields of mechanics, such as filtra tion theory, elastic-plastic problems, crystallization pro cesses, internal and surface waves, etc., is governed to a great extent by the advances in the study of free boundary problems for nonlinear partial differential equations. Free boundary problems form a scientific area which attracts attention of many specialists in mathematics and mechanics. Increasing interest in the field has given rise to the "International Conferences on Free Boundary Problems and Their Applications" which have convened, since the 1980s, in such countries as England, the United states, Italy, France and Germany. This book comprises the papers presented at the Interna tional Conference "Free Boundary Problems in Continuum Mechanics", organized by the Lavrentyev Institute of Hydrodynamics, Russian Academy of Sciences, July 15-19, 1991, Novosibirsk, Russia. The scientific committee consisted of: Co-chairmen: K.-H. Hoffmann, L.V. Ovsiannikov S. Antontsev (Russia) J. Ockendon (UK) M. Fremond (France) L. Ovsiannikov (Russia) A. Friedman (USA) S. Pokhozhaev (Russia) K.-H. Hoffmann (Germany) M. Primicerio (Italy) A. Khludnev (Russia) V. Pukhnachov (Russia) V. Monakhov (Russia) Yu. Shokin (Russia) V. Teshukov (Russia) Our thanks are due to the members of the Scientific Com mittee, all authors, and participants for contributing to the success of the Conference. We would like to express special appreciation to N. Makarenko, J. Mal'tseva and T. Savelieva, Lavrentyev Institute of Hydrodynamics, for their help in preparing this book for publication
Science Citation Index
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Author :
language : en
Publisher:
Release Date : 1993
Science Citation Index written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.
Vols. for 1964- have guides and journal lists.
Complex Hyperbolic Geometry
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Author : William Mark Goldman
language : en
Publisher: Oxford University Press
Release Date : 1999
Complex Hyperbolic Geometry written by William Mark Goldman and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Complex hyperbolic geometry is a particularly rich area of study, enhanced by the confluence of several areas of research including Riemannian geometry, complex analysis, symplectic and contact geometry, Lie group theory, and harmonic analysis. The boundary of complex hyperbolic geometry, known as spherical CR or Heisenberg geometry, is equally rich, and although there exist accounts of analysis in such spaces there is currently no account of their geometry. This book redresses the balance and provides an overview of the geometry of both the complex hyperbolic space and its boundary. Motivated by applications of the theory to geometric structures, moduli spaces and discrete groups, it is designed to provide an introduction to this fascinating and important area and invite further research and development.
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes
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Author : Boyan Sirakov
language : en
Publisher: World Scientific
Release Date : 2019-02-27
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Boyan Sirakov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Geometric Level Set Methods In Imaging Vision And Graphics
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Author : Stanley Osher
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-08
Geometric Level Set Methods In Imaging Vision And Graphics written by Stanley Osher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-08 with Computers categories.
Introduction Imageprocessing,computervisionandcomputergraphicsarenowestablished - search areas. Pattern recognition and arti?cial intelligence were the origins of the explorationofthespace ofimages.Simplistic digitaltechniquesusedatthe beg- ning of 60’s for gray image processing operations have been now replaced with a complex mathematical framework that aims to exploit and understand images in two and three dimensions. Advances in computing power continue to make the use and processing of visual information an important part of our lives. The evolution of these techniques was a natural outcome of the need to p- cess an emerging informationspace, the space of natural images. Images in space and time are now a critical part of many human activities. First, pictures and now video streams were used to eternalize small and signi?cant moments of our life. Entertainment including movies, TV-programs and video games are part of our every-day life where capturing, editing, understanding and transmitting images are issues to be dealt with. The medical sector is also a major area for the use of images. The evolution of the acquisition devices led to new ways of capturing information, not visible by the human eye. Medical imaging is probably the most established market for processing visual information[405]. Visualization of c- plex structures and automated processing towards computer aided diagnosis is used more and more by the physicians in the diagnostic process. Safety and se- rity are also important areas where images and video play a signi?cant role [432].
Hamilton S Ricci Flow
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Author : Bennett Chow
language : en
Publisher: American Mathematical Society, Science Press
Release Date : 2023-07-13
Hamilton S Ricci Flow written by Bennett Chow and has been published by American Mathematical Society, Science Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-13 with Mathematics categories.
Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.
Mathematics Of Wave Phenomena
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Author : Willy Dörfler
language : en
Publisher: Springer Nature
Release Date : 2020-10-01
Mathematics Of Wave Phenomena written by Willy Dörfler and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-01 with Mathematics categories.
Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.