Vol. 88, No. 2, 1980

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ISSN: 0030-8730
The symmetry of sessile and pendent drops

Henry Wente

Vol. 88 (1980), No. 2, 387–397

Let X denote a bounded, open, and connected subset of Rn+1(n 1) which we consider to represent the interior of a liquid drop (when n = 2). The principal result of this paper will be to show that under suitable conditions X is an axially symmetric drop in the sense that there is a vertical line (axis) such that any nonempty intersection of X with a horizontal hyperplane is an open disk whose center lies on the axis. Condition 1: X adheres to a horizontal hyperplane, Σ (i.e., X Σ = Φ but X ΣΦ), with the mean curvature, H, of the liquid-air interface, Ω, a differentiable function of the vertical coordinate and the angle of contact, α, of Ω with Σ a constant along Ω, 0 α π, (Theorem 1. 1). Condition 2: X adheres to Σ with the mean curvature a smooth function of height and the contact region of X with Σ a disk (special case of Theorem 1. 2).

Mathematical Subject Classification 2000
Primary: 49H05, 49H05
Secondary: 53A10
Received: 1 November 1979
Published: 1 June 1980
Henry Wente
Department of Mathematics
University of Toledo
Toledo OH 43605-3390
United States