Abstract
In this paper,we study the Plateau’s problem in \({\rm I\!R^{3}}\) with density and we give prove that \(div_{\varphi}\textbf{N} = -2H_{\varphi}\) in a Riemannian manifold \({\rm I\!M^{3}}\) with density Ψ = e ϕ, where H ϕ and N are the ϕ-mean curvature and the unit normal vector field of a surface S in \({\rm I\!M^{3}}\) with density.
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Belarbi, L., Belkhelfa, M. (2013). Variational Problem in Euclidean Space with Density. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_27
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DOI: https://doi.org/10.1007/978-3-642-40020-9_27
Publisher Name: Springer, Berlin, Heidelberg
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