2008/09/22 by Rafael López, López, Rafael
Engineering · Mathematics · Physics and Astronomy · #35J25 #53A10 #76U05 #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Fluid dynamics and aerodynamics studies #Planetary Science and Exploration #math.DG #msc:35J25 #msc:53A10 #msc:76U05
paper · pdf · doi:10.48550/arxiv.0809.3818
26 pages, 5 figures
arxiv created 2008/09/22 · openalex publication_date 2008/09/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
A stationary rotating surface is a compact surface in Euclidean space whose mean curvature H at each point x satisfies 2H(x)=a r2+b, where r is 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.