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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!