Resumen de Approximating symmetric capillary surfaces

David Siegel

• An iterative method is introduced for approximating symmetric capillary surfaces which makes use of the known exact volume. For the interior and annular problems this leads to upper and lower bounds at the center or inner boundary and at the outer boundary, and to an asymptotic expansion in powers of the Bond number. For the exterior problem we determine the leading order asymptotics of the boundary height as the Bond number tends to zero, obtaining a result first proved by B. Turkington.