A Note on My-stable Surfaces with Prescribed Constant Mean Curvature
Author : Steffen Fröhlich
Publisher :
Page : 7 pages
File Size : 19,63 MB
Release : 2002
Category :
ISBN :
Author : Steffen Fröhlich
Publisher :
Page : 7 pages
File Size : 19,63 MB
Release : 2002
Category :
ISBN :
Author : Steffen Fröhlich
Publisher :
Page : 7 pages
File Size : 31,50 MB
Release : 2002
Category :
ISBN :
Author : Steffen Fröhlich
Publisher :
Page : 7 pages
File Size : 12,31 MB
Release : 2002
Category :
ISBN :
Author : Steffen Fröhlich
Publisher :
Page : pages
File Size : 12,21 MB
Release : 2002
Category :
ISBN :
Author : Bennett Palmer
Publisher :
Page : 156 pages
File Size : 42,80 MB
Release : 1986
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ISBN :
Author : Mathematical Sciences Research Institute (Berkeley, Calif.).
Publisher :
Page : pages
File Size : 18,25 MB
Release : 1992
Category :
ISBN :
Author : Leung-Fu Cheung
Publisher :
Page : 124 pages
File Size : 46,39 MB
Release : 1991
Category :
ISBN :
Author : Zuhal Kucukarslan Yuzbasi
Publisher : Infinite Study
Page : 8 pages
File Size : 13,21 MB
Release : 2022-01-01
Category : Mathematics
ISBN :
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.
Author : Lawrence E. Schmidt
Publisher :
Page : 24 pages
File Size : 27,37 MB
Release : 19??
Category : Surfaces
ISBN :
Author : Katsuei Kenmotsu
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 20,42 MB
Release : 2003
Category : Mathematics
ISBN : 9780821834794
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.