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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A variational problem for surfaces in
Laguerre geometry


Authors: Emilio Musso and Lorenzo Nicolodi
Journal: Trans. Amer. Math. Soc. 348 (1996), 4321-4337
MSC (1991): Primary 58E40, 53A40, 53A05
MathSciNet review: 1370648
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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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Additional Information

Emilio Musso
Affiliation: Dipartimento di Matematica Pura ed Applicata, Università di L’Aquila, via Vetoio, I-67010 Coppito, L’ Aquila, Italy
Email: musso@axscaq.aquila.infn.it

Lorenzo Nicolodi
Affiliation: Dipartimento di Matematica “G. Castelnuovo", Università di Roma “La Sapienza", p.le A. Moro 2, I-00185 Roma, Italy
Email: nicolodi@mat.uniroma1.it

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01698-4
PII: S 0002-9947(96)01698-4
Keywords: Laguerre geometry, $L$-minimal surfaces, Legendre surfaces
Received by editor(s): June 16, 1994
Additional Notes: Partially supported by CNR contract n. 93.00554.CTO1, the GADGET initiative of the EC and MURST 40%.
Article copyright: © Copyright 1996 American Mathematical Society