The Bernstein conjecture, minimal cones and critical dimensions

Gary W. Gibbons, Keiichi Maeda, Umpei Miyamoto

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    Minimal surfaces and domain walls play important roles in various contexts of spacetime physics as well as material science. In this paper, we first review the Bernstein conjecture, which asserts that a plane is the only globally well-defined solution of the minimal surface equation which is a single valued graph over a hyperplane in flat spaces, and its failure in higher dimensions. Then, we review how minimal cones in four- and higher-dimensional spacetimes, which are curved and even singular at the apex, may be used to provide counterexamples to the conjecture. The physical implications of these counterexamples in curved spacetimes are discussed from various points of view, ranging from classical general relativity, brane physics and holographic models of fundamental interactions.

    Original languageEnglish
    Article number185008
    JournalClassical and Quantum Gravity
    Volume26
    Issue number18
    DOIs
    Publication statusPublished - 2009

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    minimal surfaces
    cones
    hyperplanes
    physics
    materials science
    domain wall
    relativity
    apexes
    interactions

    ASJC Scopus subject areas

    • Physics and Astronomy (miscellaneous)

    Cite this

    The Bernstein conjecture, minimal cones and critical dimensions. / Gibbons, Gary W.; Maeda, Keiichi; Miyamoto, Umpei.

    In: Classical and Quantum Gravity, Vol. 26, No. 18, 185008, 2009.

    Research output: Contribution to journalArticle

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