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answered Construct a diffeomorphism $\phi:M\to M$ such that $\phi(p)=q$ and also $d\phi(X_p)=Y_q$
Jun
27
comment Lift of $z^2$ map $S^1 \to S^1$
Ah, I figured "lift" meant "lifted to the universal covers." Would you mind editing your question to be clearer as to the domains and codomains of the lifts, please?
Jun
27
comment Lift of $z^2$ map $S^1 \to S^1$
The identity map $S^1\to S^1$ lifts to the identity map $\mathbb{R}\to\mathbb{R}$.
Jun
27
comment When proving that f(z) is a polynomial, is it enough to consider just one point instead of keeping z arbitrary?
Here's a hint, in lieu of an actual answer: You should be able to prove (or look up the proof in your textbook) that the CIF for entire functions doesn't actually depend on choice of integrating contour, beyond that it be a simple closed curve. From this, can you prove that the choice of basepoint doesn't matter?
Jun
27
comment When proving that f(z) is a polynomial, is it enough to consider just one point instead of keeping z arbitrary?
If two holomorphic functions on the same domain are equal on any open set in that domain, they are identically equal.
Jun
23
comment Invertibility of operator $-\Delta -\lambda_{1} I: W_{*}^{2,p}(\Omega)\rightarrow L_{*}^{p}(\Omega)$
I'm not clear on what you mean by $W^{2,p}_*$. Do you want it to be the subspace of $W^{2,p}$ with that property? (For $p=2$, the orthogonal complement of the span of a first eigenfunction.)
Jun
23
revised Divergence of $\vec{F} = \frac{\hat{\mathrm{r}}}{r^{2}}$
forgot $4\pi$
Jun
23
comment Totally geodesic hypersurface in compact hyperbolic manifold
Is there a method for dimension greater than $3$, perhaps by considering algebraic properties of lattices in $SL(n,\Bbb{R})$?
Jun
22
answered Divergence of $\vec{F} = \frac{\hat{\mathrm{r}}}{r^{2}}$
Jun
9
comment Understanding splitting lemma
First paragraph addresses your assertion directly. Next two paragraphs elaborate on why your belief is wrong. If you edit an argument for your belief that injectivity/surjectivity imply splitting into the question, I will be happy to alter my answer accordingly.
Jun
9
answered Understanding splitting lemma
Jun
7
answered dirichlet principle: why $u-g\in W_0^{1,2}(\Omega)$?
Jun
4
comment How to visualize rotation on a hyperbola?
Think of what happens when you take a beer case and collapse it into a parallelogram.
Jun
1
comment Vanishing gradient of a surface $z=f(x,y)$ by a rigid motion
@StevenVanGeluwe For $p$, take the inf over $q\in\Sigma$ of $d(p,q)$. If $\Sigma$ is closed, then for $p\notin\Sigma$ there is a $q$ where this is realized and not zero, and if $p$ is close enough to $\Sigma$ this $q$ is unique.
Jun
1
comment Instruct geometer moths so you can learn about their true geometry.
@zoli It would work to measure angle deviation in the triangle constructed in method one, but that doesn't quite seem in the spirit of your question.
Jun
1
answered Vanishing gradient of a surface $z=f(x,y)$ by a rigid motion
May
31
comment Instruct geometer moths so you can learn about their true geometry.
The construction described in the question, by the way, uses that the space is symmetric, so it cannot distinguish between the model geometries.
May
31
comment Vanishing gradient of a surface $z=f(x,y)$ by a rigid motion
The gradient is preserved by rigid motions, so this doesn't seem to make sense. Would you mind linking to the wikipedia page?
May
31
comment Instruct geometer moths so you can learn about their true geometry.
Sorry, I don't quite understand the question. Are you asking for (a) determining their geometry from the given procedure, (b) a procedure for determining a tangent that enables one to distinguish between the model geometries, or (c) something else?
May
31
comment Doubt over a real analysis problem
What have you tried? Where did you get stuck?