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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
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52
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

12
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
Coordinate independence of geometrical objects.
math.stackexchange.com

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?
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?
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10
Notation: What does this summation mean?
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10
Geometrical interpretation of Ricci curvature
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10
Prove that if a linear operator is continuous, then it is bounded.
math.stackexchange.com

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

10
Adjoint of the covariant derivative on a Riemannian manifold
math.stackexchange.com

10
Differentiability of the distance function
math.stackexchange.com

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

9
What is the motivation of Measure Theory when there is probability theory?
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
Is any map homotopic to a map having fixed point?
math.stackexchange.com

8
Is sine of angles greater than 90 degrees a convention?
math.stackexchange.com

7
A step function is right continuous with left limits
math.stackexchange.com

7
I am almost certain the book is wrong on this “proof” of a limit.
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7
Can you take out the exponent from an integral?
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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
Are all metric tensors diagonal?
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7
Are there infinitely many non equivalent metric spaces on certain sets (?)
math.stackexchange.com

7
Can we symmetrize connections on tangent bundles?
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7
Intuition on Kulkarni-Nomizu product
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