- Why is a² + b² ≥ 2ab ?
- A remark on the divergence theorem
- The Cauchy-Schwarz inequality and the Lagrange identity
- On the existence of a metric compatible with a given connection
- A curious identity on the median triangle
- 27 lines on a smooth cubic surface
- Weighted Hsiung-Minkowski formulas and rigidity of umbilic hypersurfaces
- The discrete Gauss-Bonnet theorem
- Why a vector field rotates about its curl?
- A functional inequality on the boundary of static manifolds
tong cheung yu on On the existence of a metric c… Marco Barchiesi on Simple curves with a positive… tong cheung yu on Toric perspective 1 lamwk on Why is a² + b² ≥ 2ab ? Maurice OReilly on Spherical cosine law KKK on Sobolev and Isoperimetric… Anonymous on Sobolev and Isoperimetric… tong cheung yu on On the existence of a metric c… Anonymous on Closed subspaces of a reflexiv… KKK on A curious identity on the medi…
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- Martingale Theory II: Conditional expectation
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- Mean value properties for harmonic functions on Riemannian manifolds
- A note on Obata's theorem
- Mathematics behind JPEG
- Understanding Lagrange multipliers (1)
- The Brunn-Minkowski inequality and the isoperimetric inequality
- Why does a mirror reverse left and right, but not top and bottom?
Author Archives: Hon Leung
Here describes two different proofs of a general smooth cubic surface containing exactly 27 lines. One approach uses blow-ups and the other one uses the Grassmannian. If I have time I will elaborate on the discussion.
This series of posts will be about toric varieties. The author is not sure if there is a part 2, but he still calls this part 1. This post is about computing the dimensions and degrees of popular toric varieties. … Continue reading
There are univariate polyomials that the number of non-real roots is significantly larger than that of real roots. The simplest example is where is odd. It has one real root and non-real roots. In this post we show an example … Continue reading
This is just a short remark about 3 x 3 skew-symmetric-matrix. Theorem. If is nonzero and skew-symmetric, then two of its singular values are nonzero and equal, while the other one is zero. Proof. … Continue reading
It has been a while since the last post. Let us recall what we have done. We study the unconstrained polynomial optimization problem () where is a real polynomial. This problem is equivalent to () … Continue reading
In this post we shall give another proof of the famous AM-GM-HM inequality: If are positive real numbers, then AM GM HM, precisely .