Tromba, Anthony J. <br/><br/>
On the Number of Simply Connected Minimal Surfaces Spanning a Curve. 

 - 1st ed. 
 - 1 online resource (131 pages) 
 - Memoirs of the American Mathematical Society ;  v.12 .
 - Memoirs of the American Mathematical Society .
<br/><br/>Intro -- Table of Contents -- 0. Introduction -- I. A review of the Euler characteristic of a Palais-Smale vector field -- II. Analytical preliminaries - the Sobelev spaces -- III. The global formulation of the problem of Plateau -- IV. The existence of a vector field associated to the Dirichlet functional E[sub(α)] -- V. A proof that the vector field X[sup(α)], associated to E[sub(α)], is Palais-Smale -- VI. The weak Riemannian structure on η[sub(α)] -- VII. The equivariance of X[sup(α)] under the action of the conformal group -- VIII.The regularity results for minimal surfaces -- IX. The Fréchet derivative of the minimal surface vector field X and the surface fibre bundle -- X. The minimal surface vector field X is proper on bounded sets -- XI. Non-degenerate critical submanifolds of η[sub(α)] and a uniqueness theorem for minimal surfaces -- XII. The spray of the weak metric -- XIII. The transversality theorem -- XIV. The Morse number of minimal surfaces spanning a simple closed curve and its invarience under isotopy -- XV. References. 
<br/><br/><label>ISBN: </label>9781470401559 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Minimal surfaces.<br/>Critical point theory (Mathematical analysis).<br/>Boundary value problems.
<br/><br/><label>Index Terms--Genre/Form: </label><br/>Electronic books.
<br/><br/><label>LC Class. No.: </label>QA614.7 -- .T76 1977eb 
<br/><br/><label>Dewey Class. No.: </label>510/.8 s;516/.362