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Feb 23, 2011 at 18:43 comment added ε-δ As the intersection; if $v$ is smooth, the condition on the second fundamental form implies that $M$ is on the boundary. That is true only for $p$ in a small set open domain of $M$.
Feb 15, 2011 at 21:28 comment added AndreA I am not sure I understand your construction. Let [B_p=\{x\mid \langle x,v_p\rangle\leq\langle p,v_p\rangle\}.] Is then $B$ defined as the union or intersection of all $B_p$? In the former case why is it convex, and in the latter why is $M$ in its boundary?
Feb 15, 2011 at 17:13 history answered ε-δ CC BY-SA 2.5