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math.DS2013★ 4 cited
Busemann functions and barrier functions
Xiaojun Cui, Jian cheng
We show that Busemann functions on a smooth, non-compact, complete, boundaryless, connected Riemannian manifold are viscosity solutions with respect to the Hamilton-Jacobi equation…
math.DS2013★ 1 cited
Locally Lipschitz graph property for lines
Xiaojun Cui
On a non-compact, smooth, connected, boundaryless, complete Riemannian manifold , one can define its ideal boundary by rays (or equivalently, Busemann functions). From the v…
math.DS2013
Viscosity solutions, ends and ideal boundary
Xiaojun Cui
On a smooth, non-compact, complete, boundaryless, connected Riemannian manifold , there are three kinds of objects that have been studied extensively: Viscosity so…