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The Second Periodic Eigenvalue and the Alikakos–Fusco Conjecture

✍ Scribed by Vassilis G. Papanicolaou

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
343 KB
Volume
130
Category
Article
ISSN
0022-0396

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✦ Synopsis

We investigate the maximality properties of the second periodic eigenvalue of the Hill's operator. The potential function is normalized so that its average over a period is zero. Apart from its own significance, this question is related to the study of the motion-by-curvature equation.

1996 Academic Press, Inc.

where s is the arc-length, k is the curvature, 2 X is the Laplace Beltrami operator associated to X, and k j , j=1, ..., n, are the principal curvatures of X (notice that h is assumed to be a smooth function defined on X; in the case n=1 we must have that h(0)=h(l ), where l is the length of the article no. 0146

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