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Sadofsky, Hal Munson, Brian Andrew 2026-07-31T18:55:42Z 1998 https://hdl.handle.net/1794/33191 38 pages. We model immiscible fluid clusters in space by cost-minimizing polyhedral surfaces, where “cost” is a weighted area. We also discuss planar configurations of immiscible fluid clusters modeled by costminimizing networks, where cost is a weighted length. We give necessary and sufficient conditions for local minimization of networks in the plane and cones of planes meeting along a line in space. A cone is minimizing if and only if a certain geometric upoint-placing” condition is fulfilled. We extend these results to allow a single additional fluid not present in the original configuration. It is not known whether point-placing and minimization are equivalent for cones of planes meeting at a point, but we conjecture the same point-placing condition and discuss some special examples of such minimizing configurations. en_US University of Oregon Creative Commons BY-NC-ND 4.0-US UO theses and dissertations are provided for research and educational purposes and may be under copyright by the author or the author’s heirs. Please contact scholars@uoregon.edu with any questions or comments. In your email, be sure to include the URL and title of the specific items that you are inquiring about. Immiscible fluid clusters Polyhedral surfaces Weighted length Steiner problem Cost-Minizming Networks and Polyhedral Cones Dissertation or thesisopen.access