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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
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58
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
Why do we think of a vector as being the same as a differential operator?
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?
math.stackexchange.com

11
Is the tangent bundle still a manifold if we equip it with the disjoint union topology?
math.stackexchange.com

11
Geometrical interpretation of Ricci curvature
math.stackexchange.com

11
mean curvature is trace of second fundamental form?
math.stackexchange.com

11
Coordinate independence of geometrical objects.
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
Prove that if a linear operator is continuous, then it is bounded.
math.stackexchange.com

10
Notation: What does this summation mean?
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

10
What is the geometric reason of why is the divergence of the curl of a vector field equal to zero?
math.stackexchange.com

10
Differentiability of the distance function
math.stackexchange.com

10
Intuition on Kulkarni-Nomizu product
math.stackexchange.com

9
Since the Curvature tensor depends on a connection(not metric), is it the relevant quantity to characterize the curvature of Riemannian manifolds?
math.stackexchange.com

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

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

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

8
Why is the Sasaki metric natural?
math.stackexchange.com

8
On the definition of the geodesic curvature and its relation to concepts from Riemannian geometry
math.stackexchange.com

7
Are the level sets of any norm non negatively curved?
math.stackexchange.com

7
Restriction of smooth maps between manifolds
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7
Can we symmetrize connections on tangent bundles?
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7
Isometries of $\mathbb{S}^2$
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