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Stability Analysis of Capillary Surfaces with Planar or Spherical Boundary in the Absence of Gravity

Marinov, Petko I.
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1290098654

Abstract Details

2010, Doctor of Philosophy, University of Toledo, Mathematics.
We study stable capillary surfaces with planar or spherical boundary in the absence of gravity. If the boundary of the capillary surface is embedded in a plane, we prove that the only immersed stable capillary surface is the spherical cap. The second part of this dissertation treats the case when the capillary surface lies inside the unit ball in R3 with its boundary on the unit sphere. We construct a Killing vector field for the hyperbolic metric and use it to show that if the center of mass of the region bounded between the surface and the unit sphere is at the origin, the configuration cannot be stable. As a corollary of this approach we obtain a new proof of a theorem by Barbosa and do Carmo. We also provide a new proof of the stability of spherical caps on a plane or inside of the round ball, using exotic containers.
Henry Wente, PhD (Advisor)
Robert Finn, PhD (Committee Member)
Biao Ou, PhD (Committee Member)
Mao-Pei Tsui, PhD (Committee Member)
Denis White, PhD (Committee Member)
77 p.
Mathematics
capillarity; mean curvature; elliptic operators; Killing field; Laplacian; centroid

Recommended Citations

Citations

  • Marinov, P. I. (2010). Stability Analysis of Capillary Surfaces with Planar or Spherical Boundary in the Absence of Gravity [Doctoral dissertation, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1290098654

    APA Style (7th edition)

  • Marinov, Petko. Stability Analysis of Capillary Surfaces with Planar or Spherical Boundary in the Absence of Gravity. 2010. University of Toledo, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo1290098654.

    MLA Style (8th edition)

  • Marinov, Petko. "Stability Analysis of Capillary Surfaces with Planar or Spherical Boundary in the Absence of Gravity." Doctoral dissertation, University of Toledo, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1290098654

    Chicago Manual of Style (17th edition)

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© 2010, all rights reserved.
This open access ETD is published by University of Toledo and OhioLINK.