
Recent Posts
 An inequality for functions on the plane
 Weighted isoperimetric inequalities in warped product manifolds
 FaberKrahn inequality
 Why is a² + b² ≥ 2ab ?
 A remark on the divergence theorem
 The CauchySchwarz 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 HsiungMinkowski formulas and rigidity of umbilic hypersurfaces
Meta
Recent Comments
Lawrence G Mouille on Exponential maps of Lie g… 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… Categories
 Algebra
 Algebraic geometry
 Analysis
 Applied mathematics
 Calculus
 Combinatorics
 Complex analysis
 Differential equations
 Discrete Mathematics
 Dynamical system
 Fourier analysis
 Functional analysis
 General Relativity
 Geometry
 Group theory
 Inequalities
 Linear Algebra
 Miscellaneous
 Number Theory
 Operator Theory
 Optimization
 Potential theory
 Probability
 Set Theory
 Statistics
 Topology
 Uncategorized
Top Posts
 Complex analysis  Problem solving strategies.
 Lie groups with biinvariant Riemannian metric
 Sum of angle defects of polyhedrons
 Martingale Theory II: Conditional expectation
 Some integral formulas for hypersurface in Euclidean space 2
 Some integral formulas for hypersurface in Euclidean space
 An inequality for functions on the plane
 Surjectivity of Gauss map and its degree
 Weighted isoperimetric inequalities in warped product manifolds
 The discrete GaussBonnet theorem
Archives
Author Archives: lamwk
A brief introduction to Gammaconvergence
1. A motivating example Consider the Laplace equation in , where is a nonempty bounded open subset of , and on . The energy functional associated with the PDE is . For , because of convexity, has a unique minimizer … Continue reading
Posted in Differential equations
Leave a comment
Weak L^1 is not locally convex
Let be the Lebesgue measure on . Consider , the space of Lebesgue measurable functions for which there exists some constant such that for every , . The purpose of this post is to show that this is not a … Continue reading
Posted in Functional analysis
Leave a comment
A dynamical proof of Fermat’s little theorem
If you have studied number theory (even just a little bit), you should know the Fermat’s little theorem: for any positive , and for any prime number , we have . Here I will give a proof by using a … Continue reading
Posted in Dynamical system, Number Theory
3 Comments
Poincaré recurrence theorem and its friends
The Poincaré recurrence theorem states that a dynamical system (under suitable conditions) will eventually return to a condition that is very close to the original condition. Slightly more formally, for a compact set in , if is a volume preserving … Continue reading
Posted in Dynamical system, Number Theory
Leave a comment
Mathematics behind JPEG
Many of you should have this experience: when you save a picture with many words in Paint(小畫家) as .jpg file, some ugly artifacts appear. Then you may think why is such a low quality image format so common? At the … Continue reading
Posted in Miscellaneous
Leave a comment
A dynamical proof of some Diophantine approximations
Diophantine approximations is a field in number theory which asks how good a real number can be approximated by some rational number. Quite a number of classical results are proved by using combinatorics, which is not friendly to people who … Continue reading
Posted in Dynamical system, Number Theory
2 Comments
Arithmetic progression in some subsets of $\mathbb{Z}_N$ (Part 2)
Last time I have mentioned the idea of the proof (of theorem 2). Now I continue and give a full detail here.
Posted in Fourier analysis, Number Theory
1 Comment