Laplacian Processes on Submanifolds

    Project Details

    Description

    The Laplacian controls a variety of very natural
    phenomena ranging from heat diffusion to volume
    growth. It is the purpose of this project to show
    precise bounds for specific values of measures
    such as the mean exit time for Brownian motion
    and isoperimetric inequalities for well chosen
    subsets of the submanifolds under consideration.
    The geometric structures under consideration are
    minimal (or close to minimal) submanifolds and
    minimal (or close to minimal) metric graphs. The
    bounds alluded to are obtained via comparison
    with corresponding values in constant curvature
    spaces and in other tailor-made warped product
    spaces.
    StatusFinished
    Effective start/end date01/01/199801/01/2020