bio | website | math.poly.edu/~yang |
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location | New York, New York | |
age | ||
visits | member for | 5 years |
seen | 19 hours ago | |
stats | profile views | 12,089 |
Oct 18 |
awarded | Yearling |
Oct 16 |
comment |
Regularity of the Minkowski functionnal of a convex
Use polar coordinates. |
Oct 16 |
comment |
Source needed (at final-year undergrad level) for the double cover of SO(3) by SU(2)
Yes, but without discussing the topological aspect. Uses quaternions. |
Oct 16 |
answered | Source needed (at final-year undergrad level) for the double cover of SO(3) by SU(2) |
Oct 15 |
comment |
How is this transformation related to the Legendre transform?
If you apply the Legendre transform to $-xf(x,y)$ in the $x$ variable and for fixed $y$, then you should get $s$ back. And, yes, it appears that $f$ is concave with respect to $y$ since it's obtained as an infimum over a family of concave functions. |
Oct 15 |
comment |
How is this transformation related to the Legendre transform?
It looks to me like that, for each $y$, $-xf(x,y)$ is the Legendre transform of $-s(t,y)$. |
Oct 11 |
awarded | Custodian |
Oct 11 |
reviewed | Leave Closed The periodic architecture underlying the natural numbers |
Oct 11 |
comment |
Monge-Ampere type PDE
I agree with Robert that the question (and not just a comment) should contain an explicit description of how a Riemannian metric is constructed from the function $f$. Also, I don't recognize the PDE as written as an elliptic Monge-Ampere equation as it should be. |
Oct 7 |
revised |
Variation of curvature with respect to immersion?
deleted 98 characters in body |
Oct 7 |
answered | Variation of curvature with respect to immersion? |
Oct 7 |
revised |
Variation of curvature with respect to immersion?
deleted 16 characters in body |
Oct 7 |
answered | Variation of curvature with respect to immersion? |
Oct 1 |
awarded | Favorite Question |
Oct 1 |
comment |
The relation between Gromov hausdorff convergence and inverse limit of compact metric spaces
The question could be rephrased as follows: Does there exist a subset of Euclidean space that is isometric to the Gromov-Hausdorff limit? |
Oct 1 |
comment |
Is the identification between symmetric tensors and homogeneous polynomials useful?
Sorry. I didn't read the question carefully. Your example is a question about tensors with respect to a single vector space, so it is a purely algebraic question. Differential geometry is effectively the study of tensors with respect to a smooth parameterized family of vector spaces. I don't see any need or use of differential geometry for a question like yours. |
Sep 30 |
awarded | Explainer |
Sep 30 |
comment |
Is the identification between symmetric tensors and homogeneous polynomials useful?
Arguably, the only point to tensors is as homogeneous polynomials or multilinear functions. A tensor is difficult to interpret geometrically. Typically, it's only when you evaluate it on on the right number of tangent vectors (or cotangent vectors) that you get a number that you can interpret. The most obvious example of this is the Riemann curvature tensor. I don't know any way to explain the full tensor geometrically, but if you evaluate it properly using two tangent vectors (which span a 2-d plane), then you get sectional curvature which does mean something geometrically. |
Sep 21 |
comment |
Differentiability of Nemytskii operator on Sobolev space
It seems like you're on the right track. It's just the chain rule, no? |
Sep 21 |
comment |
Did differential geometry undergo a notation change?
Thomas, that's a really good point! The ordering of the indices of the curvature tensor is a confusing issue. It took me a long time to figure out the "right" way to order the indices and how to justify it. |