Download or read book Absolute Gradient Bounds for Surfaces of Constant Mean Curvature written by KokSeng Chua and published by . This book was released on 1988 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Surfaces with Constant Mean Curvature written by Katsuei Kenmotsu and published by American Mathematical Soc.. This book was released on 2003 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the three-dimensional space. A surface whose mean curvature is zero at each point is a minimal surface, and it is known that such surfaces are models for soap film. There is a rich and well-known theory of minimal surfaces. A surface whose mean curvature is constant but nonzero is obtained when we try to minimize the area of a closed surface without changing the volume it encloses. An easy example of a surface of constant mean curvature is the sphere. A nontrivial example is provided by the constant curvature torus, whose discovery in 1984 gave a powerful incentive for studying such surfaces. Later, many examples of constant mean curvature surfaces were discovered using various methods of analysis, differential geometry, and differential equations. It is now becoming clear that there is a rich theory of surfaces of constant mean curvature. In this book, the author presents numerous examples of constant mean curvature surfaces and techniques for studying them. Many finely rendered figures illustrate the results and allow the reader to visualize and better understand these beautiful objects. The book is suitable for advanced undergraduates, graduate students and research mathematicians interested in analysis and differential geometry.

Download or read book Comparison Methods and Stability Theory written by Xinzhi Liu and published by CRC Press. This book was released on 2020-12-17 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is based on the International Symposium on Comparison Methods and Stability Theory held in Waterloo, Ontario, Canada. It presents advances in comparison methods and stability theory in a wide range of nonlinear problems, covering a variety of topics such as ordinary, functional, impulsive, integro-, partial, and uncertain differential equations.

Download or read book Surfaces of Constant Mean Curvature in Space Forms written by Bennett Palmer and published by . This book was released on 1986 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Surfaces of Constant Mean Curvature in Constant Curvature Manifolds written by D. Hoffmann and published by . This book was released on 1971 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Infinite Boundary Value Problems for Surfaces of Constant Mean Curvature written by Joel Spruck and published by . This book was released on 1971 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Indiana University Mathematics Journal written by Indiana University. Department of Mathematics and published by . This book was released on 1992 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Compactness and gradient bounds for solutions of the mean curvature system in two independent variables written by Giovanni Gregori and published by . This book was released on 1992 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Parametric Surfaces with Constant Mean Curvature Along Given Smarandache Curves in Lie Group written by Zuhal Kucukarslan Yuzbasi and published by Infinite Study. This book was released on 2022-01-01 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper finds sufficient conditions to determine a surface whose mean curvature along a given Smarandache curve is constant in a three-dimensional Lie group. This is accomplished by using the Frenet frames of the specified curve to express surfaces that span the 𝑇𝑁, 𝑁𝐵, and 𝑇𝐵 Smarandache curves parametrically. In terms of the curvatures of given Smarandache curves, marching scale functions, and their partial derivatives, the mean curvatures of these surfaces along the given 𝑇𝑁, 𝑁𝐵, and 𝑇𝐵 Smarandache curves are determined. Sufficient conditions are found to maintain the provided mean curvatures of the resulting surfaces at a constant value. Finally, some examples are provided.

Download or read book Compactness and Gradient Bounds for Solutions of the Mean Curvature System in Two Independent Variabes written by and published by . This book was released on 1992 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Existence of Surfaces of Constant Mean Curvature with Free Boundaries written by M. Struwe and published by . This book was released on 1986 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Concerning Surfaces with Constant Negative Curvature written by Albert Victor Bäcklund and published by . This book was released on 1899 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Regularity of Minimal Surfaces written by Ulrich Dierkes and published by Springer Science & Business Media. This book was released on 2010-08-16 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is that, for principal reasons, it is impossible to derive a priori estimates. Therefore regularity proofs for non-minimizers have to be based on indirect reasoning using monotonicity formulas. This is followed by a long chapter discussing geometric properties of minimal and H-surfaces such as enclosure theorems and isoperimetric inequalities, leading to the discussion of obstacle problems and of Plateau ́s problem for H-surfaces in a Riemannian manifold. A natural generalization of the isoperimetric problem is the so-called thread problem, dealing with minimal surfaces whose boundary consists of a fixed arc of given length. Existence and regularity of solutions are discussed. The final chapter on branch points presents a new approach to the theorem that area minimizing solutions of Plateau ́s problem have no interior branch points.

Download or read book Surfaces with Constant Mean Curvature written by Lawrence E. Schmidt and published by . This book was released on 19?? with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Minimal Surfaces and Functions of Bounded Variation written by Giusti and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which received a satis factory solution only in recent years. Called the problem of Plateau, after the blind physicist who did beautiful experiments with soap films and bubbles, it has resisted the efforts of many mathematicians for more than a century. It was only in the thirties that a solution was given to the problem of Plateau in 3-dimensional Euclidean space, with the papers of Douglas [DJ] and Rado [R T1, 2]. The methods of Douglas and Rado were developed and extended in 3-dimensions by several authors, but none of the results was shown to hold even for minimal hypersurfaces in higher dimension, let alone surfaces of higher dimension and codimension. It was not until thirty years later that the problem of Plateau was successfully attacked in its full generality, by several authors using measure-theoretic methods; in particular see De Giorgi [DG1, 2, 4, 5], Reifenberg [RE], Federer and Fleming [FF] and Almgren [AF1, 2]. Federer and Fleming defined a k-dimensional surface in IR" as a k-current, i. e. a continuous linear functional on k-forms. Their method is treated in full detail in the splendid book of Federer [FH 1].

Download or read book Regularity for stationary surfaces of constant mean curvature with free boundaries written by Michael Grüter and published by . This book was released on 1984 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Rendiconti del Seminario matematico della Universit di Padova written by Università di Padova. Seminario matematico and published by . This book was released on 2003 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: