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Results tagged with dg.differential-geometry
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user 123448
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
1
vote
1
answer
425
views
A distribution $u$ such that all of its derivatives are of order zero is smooth
I'm reading Demailly's Complex Analytic and Differential Geometry In Section I.2.D.4 he uses the following fact: Suppose $u \in \mathcal{D}'(\Omega)$, where $\Omega \subset \mathbb{R}^n$ is a distribu …
- 1,141
3
votes
0
answers
132
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Restriction of complete 1-forms to closed submanifolds (Sharpe's book on Cartan geometries)
In his Book Differential Geometry: Cartan's generalization of Klein's Erlangen Program, Sharpe gives the following definition of a complete 1-form:
Soon thereafter he gives the following example:
I …
- 1,141
4
votes
0
answers
101
views
Serre vanishing on one-point blow-ups
This is basically the last step of problem 5.3.7 in Huybrechts' Complex Geometry.
Let $X$ be a complex manifold, $x \in X$, $E$ a holomorphic vector bundle on $X$ and $L$ a positive line bundle. Denot …
- 1,141
3
votes
1
answer
1k
views
Friedrichs mollifiers and Sobolev spaces
$\renewcommand{\epsilon}{\varepsilon}$The following is from John Roe's book Elliptic operators, topology and asymptotic methods. $S$ is a vector bundle on a compact manifold $M$, but I think for my qu …
- 1,141