1,023 reputation
216
bio website
location Hangzhou, China
age 22
visits member for 1 year, 8 months
seen Jul 2 at 4:27

I'm just a guy learning and enjoying in math. My name in MO is yizhongxunhuan. Which in Chinese means a recycle.


Jul
2
awarded  Curious
May
26
awarded  Revival
May
20
comment Reference request-What is the prerequisite of S.S.Chern's proof of the generalised Gauss-Bonnet theorem?
Oh, BTW, the 2-dimensional case can be proved by Chern-Weil theory, as it is a well-known fact that all 2-real-dim'l Riemannian manifolds are Riemann surfaces.
May
20
comment Reference request-What is the prerequisite of S.S.Chern's proof of the generalised Gauss-Bonnet theorem?
I only know that the Chern-Weil theory will give the G-B-C theorem for complex manifolds. The way I know to get Pfaffian is that from Mathai-Quillen's geometric construction of Thom classes.
May
20
comment Reference request-What is the prerequisite of S.S.Chern's proof of the generalised Gauss-Bonnet theorem?
It seems hard to get Pfaffian from Chern-Weil theory? Isn't Chern-Weil assume the bundle tobe complex vector bundle, and I think the tangent bundle of arbitrary real manifold won't admit a complex vector bundle structure.
May
13
asked Two books defined two Chern(Euler) classes yet differed by a negative sign, what's wrong?
Mar
28
accepted How much of an $n$-dimensional manifold can we embed into $\mathbb{R}^n$?
Mar
23
accepted Total mean curvature of an immersed torus.
Mar
21
accepted Is every separately continuous function on $R^2$ continuous?
Mar
20
asked Is every separately continuous function on $R^2$ continuous?
Mar
20
comment Total mean curvature of an immersed torus.
Oh great. I don't quite understand your last paragraph, could you expand a little bit? I don't understand why when t goes to infinity the Willmore energy will be bigger than $4pi$. And by last sentence do you mean that if we have one point that has a fiber have k points then the Willmore energy will more than $4pi k$? Why so? I can't see directly from the formula above.
Feb
20
comment To express a integrable function as difference.
Oh, sorry for my mistake. I just want f=g-h almost everywhere. Will the proposition be correct this time?
Feb
20
revised To express a integrable function as difference.
added 18 characters in body
Feb
18
comment To express a integrable function as difference.
@TooOldForMath $g_n$ should be continuous...
Feb
18
asked To express a integrable function as difference.
Feb
3
accepted How to use Minkowski's formula to prove Liebmann's theorem?
Jan
26
comment How to use Minkowski's formula to prove Liebmann's theorem?
Sorry I didn't reply immediately, but in the question we only know that K is constant. So your second equation seems a little confusing as you assumed that H is constant?
Dec
17
comment Total mean curvature of an immersed torus.
Willmore conjecture won't apply to this, as pi is smaller than 4... There must be something to do with the self intersection.
Dec
1
accepted Function everywhere left continuous yet not right continuous everywhere?
Dec
1
comment Function everywhere left continuous yet not right continuous everywhere?
Ooohps, sorry, I mean not at each point. Thanks for pointing out.