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 Jul 24 comment Is the boundedness necessary to extend harmonically? Why are the conditions different between harmonic functions and holomorphic function? Jul 24 comment Is the boundedness necessary to extend harmonically? So a priori, you don't need to know $v$ is bounded. As long as $v(z) \leq o(\log |z|)$, it will be still true that $v_\epsilon(z)$ will go to $-\infty$. It is the analysis that forced $v$ to be bounded. That means, the statement can be weakened as: "if $u$ is harmonic in the punctured disk and $u(z) \leq o(\log |z|)$, then $u$ can be extended harmonically at the origin." Jul 20 revised equation of projection onto hyperplane edited body Jul 20 answered equation of projection onto hyperplane Jul 20 comment Define a relation — with functions and derivatives Let me just remark that in your case, a relation $D$ on $F$ means $D$ is a relation from $F$ to $F$, or, $D\subset F\times F$. Also, personally I would prefer not to use the words "domain" and "range". "domain" gives people a sense that you need to associate everything in it with something in the range, which is not the case in relation. It also might help if you just run some tests before you jump into the problem. For example, is $x^2 Dx$? Is $e^xDe^x+1$? Jun 30 comment second fundamental form and connection forms I guess what the author meant by "orthonormal frame" is orthonormal list of vector fields induced from local parametrization. Jun 30 awarded Inquisitive Jun 29 asked second fundamental form and connection forms Jun 24 accepted why does Lie bracket of two coordinate vector fields always vanish? Jun 24 comment why does Lie bracket of two coordinate vector fields always vanish? @JamesS.Cook, sure, that I agree. Thanks with the help. Jun 24 comment why does Lie bracket of two coordinate vector fields always vanish? @JamesS.Cook, "Let's see, if the commutator is nontrivial then I don't think that means it is not possible. I certainly can find vector fields on the plane which have nontrivial Lie Bracket." I meant vector fields with nontrivial commutator can't be coordinate derivations. Jun 24 comment why does Lie bracket of two coordinate vector fields always vanish? @JamesS.Cook, so this in a sense tells me if I start out with two vector fields such that the Lie bracket doesn't vanish, then there is no way I could find a coordinate system such that they happen to be coordinate derivations. Now, is the reverse true? That is, if I start out with two vector fields such that the Lie bracket DOES vanish, is it true that I can find a coordinate system with them being coordinate derivations? Thanks! Jun 24 asked why does Lie bracket of two coordinate vector fields always vanish? Mar 25 accepted borel measurable functions and measurable functions Mar 25 comment borel measurable functions and measurable functions Thanks! Very neat construction! Mar 25 comment borel measurable functions and measurable functions @PhoemueX Thanks, that solves the problem! Mar 25 asked borel measurable functions and measurable functions Mar 13 awarded Yearling Feb 7 accepted boundary of the support of a continuous function Feb 7 comment boundary of the support of a continuous function Thanks. That's a nice example!