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In a recent paper [17] we studied asymmetric metric spaces; in this context we studied the length of paths, introduced the class of run-continuous paths; and noted that there are different definitions of “length spaces” (also known as “path-metric spaces” or “intrinsic spaces”). In this paper we continue the analysis of asymmetric metric spaces.We propose possible definitions of completeness and (local)...
We formulate an Hamilton–Jacobi partial differential equation $$H(x,Du(x))=0$$ on a n dimensional manifold M, with assumptions of convexity of the sets $\{p:H(x,p)\le 0\}\subset T^{*}_{x}M$ , for all x. We reduce the above problem to a simpler problem; this shows that u may be built using an asymmetric distance (this is a generalization of the “distance function” in Finsler geometry); this...
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