Abstract
Suppose in ℝ3 there are several adjoining but not mixing physical media, for instance, in a large vessel there are several immiscible fluids. Suppose, the whole system is in equilibrium. Since the media are immiscible, the boundaries (interfaces) between them are determined. These interfaces J can be tought of (in the first approximation) as two-dimensional piece-wise smooth surfaces separating the adjoining media. We consider for simplicity the case of two media which we denote by A1 and A2. Let the pressures in the media be respectively equal to p1 and p2. The equilibrium condition for the media proves to impose a strong restriction upon the geometry of their interface. To formulate this restriction, we require an important concept of local differential geometry, namely, the concept of mean curvature of the surface.
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© 1994 Springer-Verlag Berlin Heidelberg
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Fomenko, A.T. (1994). Visual Images in Some Other Fields of Geometry and in Its Applications. In: Visual Geometry and Topology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76235-2_4
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DOI: https://doi.org/10.1007/978-3-642-76235-2_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-76237-6
Online ISBN: 978-3-642-76235-2
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