Stack Exchange

Anthony Carapetis

Canberra ACT, Australia

http://a.carapetis.com/math

PhD in geometric analysis. My thesis research focused on geometric heat flows of maps between manifolds. More broadly, I'm interested in both the theory and visualization of differential geometry.

Now working as a software engineer. Will integrate by parts for a postdoc.

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Top Questions
Top Answers
68
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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29
Why do we think of a vector as being the same as a differential operator?
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19
Intuition on Kulkarni-Nomizu product
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17
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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16
mean curvature is trace of second fundamental form?
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16
Prove that if a linear operator is continuous, then it is bounded.
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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
Isometry of Torus
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15
If a plane curve has curvature bounded from below, is it contained in a disk?
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15
Kato's inequality
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15
Adjoint of the covariant derivative on a Riemannian manifold
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15
Lie vs. covariant derivative: Visual motivation
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14
divergence of a vector field on a manifold
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14
Why is the Sasaki metric natural?
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13
Geometrical interpretation of Ricci curvature
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13
Notation: What does this summation mean?
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13
Shortest path between two points on a surface
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13
Is this contraction of metric tensor derivatives symmetric?
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12
Differentiability of the distance function
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12
Coordinate independence of geometrical objects.
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12
Is the tangent bundle still a manifold if we equip it with the disjoint union topology?
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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
Restriction of smooth maps between manifolds
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11
Second (and higher) derivatives of maps between manifolds
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11
What is the motivation of Measure Theory when there is probability theory?
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11
Commutator of laplacian and covariant derivative of a tensor
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11
When does gradient flow not converge?
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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
Is there an operation on matrices such that the determinant yields a homomorphism with the additive group of the reals?
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