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
67
Understanding the Laplace operator conceptually
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52
What is the flaw in my thinking for the graph of this function?
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25
Why do we think of a vector as being the same as a differential operator?
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17
Intuition on Kulkarni-Nomizu product
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16
Is the Lie bracket of a Lie Algebra of a Matrix Lie Group always the commutator?
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16
Prove that if a linear operator is continuous, then it is bounded.
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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
mean curvature is trace of second fundamental form?
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13
Kato's inequality
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13
divergence of a vector field on a manifold
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13
Is this contraction of metric tensor derivatives symmetric?
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13
Geometrical interpretation of Ricci curvature
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13
Adjoint of the covariant derivative on a Riemannian manifold
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13
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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12
Shortest path between two points on a surface
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12
Notation: What does this summation mean?
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12
Coordinate independence of geometrical objects.
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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 the tangent bundle still a manifold if we equip it with the disjoint union topology?
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11
Differentiability of the distance function
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11
Why is the Sasaki metric natural?
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11
Second (and higher) derivatives of maps between manifolds
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11
why not the Ricci tensor is the contraction of first and second indices of Riemann tensor
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10
Commutation of covariant derivative of functions
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10
When does gradient flow not converge?
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10
Commutator of laplacian and covariant derivative of a tensor
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10
Restriction of smooth maps between manifolds
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10
Are all metric tensors diagonal?
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10
Lie vs. covariant derivative: Visual motivation
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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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