- 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
- Complex analysis - Problem solving strategies.
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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: leonardwong
This post is written in spirit of Terrance Tao’s post on problem solving strategies in real analysis. Our emphasis will be on concrete techniques with plenty of examples (many are taken from past prelim questions in UW).
First we recall the statement of Schwarz’s lemma, which is a basic result in complex analysis. Let be the unit disk in . Schwarz’s lemma. Let . If for all and , then , and for all . If or … Continue reading
In this sequence of posts I will present a probabilistic solution of the classical Dirichlet problem using Brownian motion. I will follow the structure of the book Green, Brown and Probability and Kai-Lai Chung with some little changes and somewhat … Continue reading
This post is a sequel to Exercises in Real Analysis. 4. Let be the triangle , and be the restriction of the planar Lebesgue measure on . Suppose that . Prove that . Solution. Assume on the contrary that . … Continue reading
In this post I type up solutions of some interesting questions in the real analysis qualifying examinations. Most questions will be from UW. This post will be updated continuously. Of course, you are encouraged to think about the question before … Continue reading
This is a sequel to Martingale Theory II: Conditional Expectation. Our aim here is to prove the main theorems about discrete time martingales. More advanced probability texts (e.g. those on stochastic calculus) assume that these theorems are well known to … Continue reading