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Frank Morgan

  1. Isoperimetric Pentagonal Tilings.

    Tue, 11/29/2011 - 15:01 — SomNambul
    Authors: Frank Morgan, Ping Ngai Chung, Miguel A. Fernandez, Yifei Li, Michael Mara, Isamar Rosa Plata, Niralee Shah, Luis Sordo Vieira, Elena Wikner
    Subjects: Metric Geometry
    Abstract

    We identify least-perimeter unit-area tilings of the plane by convex
    pentagons, namely tilings by Cairo and Prismatic pentagons, find infinitely
    many, and prove that they minimize perimeter among tilings by convex polygons
    with at most five sides.

  2. Steiner and Schwarz symmetrization in warped products and fiber bundles with density.

    Wed, 11/11/2009 - 16:01 — SomNambul
    Authors: Frank Morgan, Sean Howe, Nate Harman
    Subjects: Differential Geometry
    Abstract

    We provide very general symmetrization theorems in arbitrary dimension and
    codimension, in products, warped products, and certain fiber bundles such as
    lens spaces, including Steiner, Schwarz, and spherical symmetrization and
    admitting density.

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