Deformations of Symmetric CMC Surfaces in the 3-Sphere
نویسندگان
چکیده
In this paper we numerically construct CMC deformations of the Lawson minimal surfaces ξg,1 using a spectral curve and a DPW approach to CMC surfaces in spaceforms.
منابع مشابه
On Infinitesimal Deformations of Cmc Surfaces of Finite Type in the 3-sphere
We describe infinitesimal deformations of constant mean curvature surfaces of finite type in the 3-sphere. We use Baker-Akhiezer functions to describe such deformations, as well as polynomial Killing fields and the corresponding spectral curve to distinguish between isospectral and non-isospectral deformations.
متن کاملCompact Constant Mean Curvature Surfaces with Low Genus
We describe numerical experiments that suggest the existence of compact constant mean curvature surfaces. Our surfaces come in three dihedrally symmetric families with the genus ranging from 3 to 5, 7 to 10, and 3 to 9, respectively; there are further surfaces with the symmetry of the Platonic polyhedra and genera 6, 12, and 30. We use the algorithm of Oberknapp and the second author that defin...
متن کاملLoop Group Methods for Constant Mean Curvature Surfaces
Introduction This is an elementary introduction to a method for studying harmonic maps into symmetric spaces, and for studying constant mean curvature (CMC) surfaces, that was developed by J. Dorfmeister, F. Pedit and H. Wu, and is often called the DPW method after them. There already exist a number of other introductions to this method, but all of them require a higher degree of mathematical s...
متن کاملOn the Moduli Spaces of Embedded Constant Mean Curvature Surfaces with Three or Four Ends
We are interested in explicitly parametrizing the moduli spaces Mg,k of embedded surfaces in R with finite genus g and a finite number of ends k having constant mean curvature. By rescaling we may assume this constant is 1, the mean curvature of the unit sphere. Two surfaces in R are indentified as points inMg,k if there is isometry of R carrying one surface to the other. Moreover, we shall inc...
متن کاملInstability of constant mean curvature surfaces of revolution in spherically symmetric spaces
We study the stability properties of constant mean curvature (CMC) surfaces of revolution in general simply-connected spherically symmetric 3-spaces, and in the particular case of a positive-definite 3dimensional slice of Schwarzschild space. We derive their Jacobi operators, and then prove that closed CMC tori of revolution in such spaces are unstable, and finally numerically compute the Morse...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Experimental Mathematics
دوره 24 شماره
صفحات -
تاریخ انتشار 2015