| 概要 |
We study convexity preserving properties for a class of time-dependent Hamilton-Jacobi
equations in geodesic metric spaces. Convexity preserving properties for nonlinear evolution
equations are well known in the Euclidean space. We extend the classical results for
first order equations to the Busemann spaces by using a recently developed theory of viscosity
solutions on geodesic spaces. We provide two different approaches and discuss several
generalizations for more general geodesic spaces. This talk is based on joint work with A. Nakayasu.
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