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 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
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 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
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Category Archives: Combinatorics
The discrete GaussBonnet theorem
This is a slight extension of my previous note on discrete GaussBonnet theorem. As mentioned in that note, this is a generalization of the wellknown fact that the sum of the exterior angles of a polygon is always , which … Continue reading
Posted in Calculus, Combinatorics, Discrete Mathematics, Geometry, Topology
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Toric perspective 1
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
Posted in Algebraic geometry, Combinatorics
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A Fibonaccilike sequence
What’s the pattern of the following sequence? Can you guess the next term? The answer is
Posted in Algebra, Combinatorics
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Some thoughts on 1+2+3+…
This post is a rather dumb one – and, contrary to the title, the emphasis is not on . In fact, I just put some of my dumb thoughts here after reading a comment of Terry Tao in his own … Continue reading
Posted in Combinatorics
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