A variational problem for surfaces in Laguerre geometry

Musso, Emilio; Nicolodi, Lorenzo

doi:10.1090/S0002-9947-96-01698-4

A variational problem for surfaces in Laguerre geometry
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by Emilio Musso and Lorenzo Nicolodi PDF

Trans. Amer. Math. Soc. 348 (1996), 4321-4337 Request permission

Abstract:

We consider the variational problem defined by the functional $\int {\frac {{H^{2}-K}}{{K}}}dA$ on immersed surfaces in Euclidean space. Using the invariance of the functional under the group of Laguerre transformations, we study the extremal surfaces by the method of moving frames.

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