bio | website | math.poly.edu/~yang |
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location | New York, New York | |
age | ||
visits | member for | 4 years, 6 months |
seen | 9 hours ago | |
stats | profile views | 11,164 |
Apr 17 |
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Estimate infinity norm with Lp and W1p norm
Delio, yes, you're right. I didn't notice the dimension. |
Apr 16 |
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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 |
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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
added 489 characters in body |
Apr 15 |
answered | Normal coordinates near the boundary |
Apr 15 |
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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 |
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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 |
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Young transform reference
Maybe Rockafellar's book "Convex Analysis"? |
Apr 5 |
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Bounded Ricci curvature implies bound on Jacobi determinant?
Look up the Bishop-Gromov inequality to get bounds in one direction. |
Mar 30 |
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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 |
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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 |
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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 |
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Analytic version of the Cartan lemma
Ah, good point. |
Mar 29 |
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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 |
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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
deleted 451 characters in body |
Mar 21 |
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Elliptic theory on compact manifolds
I will post a more detailed proof when I find the time, but I encourage you to try to figure out how to put all the pieces together yourself. |
Mar 20 |
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Interpolation with time continuity
What do you mean by "similar" or "more general"? |
Mar 20 |
revised |
Elliptic theory on compact manifolds
added 484 characters in body |
Mar 20 |
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Elliptic theory on compact manifolds
Sorry. What I said isn't quite right. |