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Stack Exchange

Anthony Carapetis

Canberra, Australia

http://a.carapetis.com/math

I'm a PhD student in geometric analysis at the ANU. My research focuses on geometric heat flows, particularly harmonic map heat flow and similar second-order equations.

Favourite inequality: Peter-Paul.
Differential Geometry tip: switch notations at least twice per line.
Fatal flaw: Semicolon addiction.

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Top Questions
Top Answers
55
Understanding the Laplace operator conceptually
math.stackexchange.com

51
What is the flaw in my thinking for the graph of this function?
math.stackexchange.com

14
If a plane curve has curvature bounded from below, is it contained in a disk?
math.stackexchange.com

13
Is the Lie bracket of a Lie Algebra of a Matrix Lie Group always the commutator?
math.stackexchange.com

12
Shortest path between two points on a surface
math.stackexchange.com

11
$f:\bf S^1 \to \bf R$, there exist uncountably many pairs of distinct points $x$ and $y$ in $\bf S^1$ such that $f(x)=f(y)$? (NBHM-2010)
math.stackexchange.com

11
Is this contraction of metric tensor derivatives symmetric?
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11
Is the tangent bundle still a manifold if we equip it with the disjoint union topology?
math.stackexchange.com

11
Coordinate independence of geometrical objects.
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11
Why do we think of a vector as being the same as a differential operator?
math.stackexchange.com

11
mean curvature is trace of second fundamental form?
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10
Prove that if a linear operator is continuous, then it is bounded.
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10
Adjoint of the covariant derivative on a Riemannian manifold
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10
Differentiability of the distance function
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10
Notation: What does this summation mean?
math.stackexchange.com

10
Geometrical interpretation of Ricci curvature
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10
Is there an operation on matrices such that the determinant yields a homomorphism with the additive group of the reals?
math.stackexchange.com

10
why not the Ricci tensor is the contraction of first and second indices of Riemann tensor
math.stackexchange.com

9
What is the geometric reason of why is the divergence of the curl of a vector field equal to zero?
math.stackexchange.com

9
What is the motivation of Measure Theory when there is probability theory?
math.stackexchange.com

9
Is any map homotopic to a map having fixed point?
math.stackexchange.com

8
Is sine of angles greater than 90 degrees a convention?
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7
Can you take out the exponent from an integral?
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7
I am almost certain the book is wrong on this “proof” of a limit.
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7
The Ricci flow and $\frac{\partial}{\partial t}g_{ij}=-2(R_{ij}+\nabla_i \nabla_j f)$ are equivalent up to diffeomorphism
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7
A step function is right continuous with left limits
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7
Are all metric tensors diagonal?
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7
Why is the Sasaki metric natural?
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7
Can we symmetrize connections on tangent bundles?
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7
Intuition on Kulkarni-Nomizu product
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