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
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51
What is the flaw in my thinking for the graph of this function?
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15
If a plane curve has curvature bounded from below, is it contained in a disk?
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14
Why do we think of a vector as being the same as a differential operator?
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13
Is the Lie bracket of a Lie Algebra of a Matrix Lie Group always the commutator?
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12
Shortest path between two points on a surface
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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)
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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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11
Geometrical interpretation of Ricci curvature
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11
mean curvature is trace of second fundamental form?
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11
Coordinate independence of geometrical objects.
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10
why not the Ricci tensor is the contraction of first and second indices of Riemann tensor
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10
Adjoint of the covariant derivative on a Riemannian manifold
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10
Prove that if a linear operator is continuous, then it is bounded.
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10
Notation: What does this summation mean?
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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?
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10
What is the geometric reason of why is the divergence of the curl of a vector field equal to zero?
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10
Differentiability of the distance function
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10
Intuition on Kulkarni-Nomizu product
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9
Is any map homotopic to a map having fixed point?
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9
Since the Curvature tensor depends on a connection(not metric), is it the relevant quantity to characterize the curvature of Riemannian manifolds?
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9
What is the motivation of Measure Theory when there is probability theory?
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8
Is sine of angles greater than 90 degrees a convention?
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8
Are all metric tensors diagonal?
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8
On the definition of the geodesic curvature and its relation to concepts from Riemannian geometry
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8
Why is the Sasaki metric natural?
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8
Does space of Riemannian metric on Torus and on coffee mug coincide?
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7
Restriction of smooth maps between manifolds
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7
Can we symmetrize connections on tangent bundles?
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