Geodesic
Extremal metrics for eigenvalues of the Laplace--Beltrami operator on surfaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 68 (2013) no. 6, pp. 1073-1130

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Known results on geometric optimisation of eigenvalues of the Laplace operator are briefly reviewed, and a more detailed survey of recent results in the theory of extremal metrics on surfaces is presented. Bibliography: 78 titles.
Keywords: geometric optimisation of eigenvalues, extremal metrics, minimal surfaces in spheres. 
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     author = {A. V. Penskoi},
     title = {Extremal metrics for eigenvalues of the {Laplace--Beltrami} operator on surfaces},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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A. V. Penskoi. Extremal metrics for eigenvalues of the Laplace--Beltrami operator on surfaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 68 (2013) no. 6, pp. 1073-1130. http://geodesic.mathdoc.fr/item/RM_2013_68_6_a2/