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2h
awarded  Revival
3h
revised Uniform bound on the eigenfunctions of the Laplacian
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3h
answered Uniform bound on the eigenfunctions of the Laplacian
4h
comment Uniform bound on the eigenfunctions of the Laplacian
I believe this can be done in a relatively straightforward fashion using Moser iteration.
Apr
17
comment Estimate infinity norm with Lp and W1p norm
Delio, yes, you're right. I didn't notice the dimension.
Apr
16
comment Estimate infinity norm with Lp and W1p norm
Also, the inequality does not hold for all $p \ge 1$. $p$ must be greater than $n$. You can see this by testing the inequality with $f = r^{-\alpha}$.
Apr
16
comment Estimate infinity norm with Lp and W1p norm
Roughly, yes, but your exponents are wrong. You can always figure out what the exponents should be by considering how both sides scale when you rescale $f$ or space. The exponents do have to add up to $1$ as yours do. But when you consider what happens when you rescale space, you don't get $(p-1)/p$ and $1/p$ but $1-a$ and $a$ for another value of $a$.
Apr
15
revised Normal coordinates near the boundary
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Apr
15
answered Normal coordinates near the boundary
Apr
15
comment Canonical relations and phase functions of a Fourier Integral Operator
Have you looked at any references on Fourier integral operators? This is explained in any such reference.
Apr
15
comment Normal coordinates near the boundary
You want geodesic normal or exponential coordinates relative to a hypersurface or submanifold. It should be in many texts. I would try Jost or Gallot-Hulin-Lafontaine.
Apr
9
comment Young transform reference
Maybe Rockafellar's book "Convex Analysis"?
Apr
5
comment Bounded Ricci curvature implies bound on Jacobi determinant?
Look up the Bishop-Gromov inequality to get bounds in one direction.
Mar
30
comment Geometric interpretation of Euler's identity for homogeneous functions
You derivation of the identity is the geometric interpretation. If a function is homogeneous, then you know what its derivative in the radial direction is.
Mar
29
comment Analytic version of the Cartan lemma
A more general condition is that there exists a global vector field $v$ such that $\gamma = i(v)\beta$ never vanishes.
Mar
29
comment Analytic version of the Cartan lemma
If there exists a global analytic vector field $v$ such that $\langle\alpha,v\rangle$ never vanishes, then $\gamma = i(v)\beta$ works.
Mar
29
comment Analytic version of the Cartan lemma
Ah, good point.
Mar
29
comment Analytic version of the Cartan lemma
Probably the easiest way to verify this is to choose local co-ordinates such that $\alpha = f\,dx^1$.
Mar
28
comment What is the meaning of Yang-Mills action evaluated on Levi-Civita connection?
If you google "L2 norm of curvature", you'll find some papers regarding this functional, especially in dimension 4.
Mar
21
revised Elliptic theory on compact manifolds
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