TITLE

# Stationary rotating surfaces in Euclidean space

AUTHOR(S)
López, Rafael
PUB. DATE
November 2010
SOURCE
Calculus of Variations & Partial Differential Equations;Nov2010, Vol. 39 Issue 3/4, p333
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
stationary rotating surface is a compact surface in Euclidean space whose mean curvature H at each point x satisfies 2 H( x) = a r( x) + b, where r( x) denotes the distance from x to a fixed straight-line L, and a and b are constants. These surfaces are solutions of a variational problem that describes the shape of a drop of incompressible fluid in equilibrium by the action of surface tension when it rotates about L with constant angular velocity. The effect of gravity is neglected. In this paper we study the geometric configurations of such surfaces, focusing the relationship between the geometry of the surface and the one of its boundary. As special cases, we will consider two families of such surfaces: axisymmetric surfaces and embedded surfaces with planar boundary.
ACCESSION #
54354950

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