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Results tagged with geometric-analysis
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user 20302
3
votes
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Riemannian Measures, Densities and Radon–Nikodym Theorem
This follows from the usual Radon-Nikodym theorem. Observe that, given two metrics $g_0,g_1$ on $M$ with volume densities $dV_{g_0}$, $dV_{g_1}$ then there exists a positive smooth function $\rho_ …
- 34.7k
16
votes
Sheaf-theoretically characterize a Riemannian structure?
Suppose that $M$ is a smooth manifold and $g_0, g_1$ are Riemann metrics on $M$. $\newcommand{\eH}{\mathscr{H}}$ Denote by $\eH_{g_i}$, $i=0,1$ and the sheaf of $g_i$-harmonic functions. More precise …
- 34.7k
0
votes
Is there a combinatorial analogue of the Kazdan Warner theorem?
I think that you need to state very clearly what you mean by triangulation of the manifold, and what do you mean by "angles". (On a manifold that would require a choice of metric.) If by triangu …
- 34.7k
4
votes
Volume comparison on Grassmannian
$\DeclareMathOperator{\Gr}{Gr}$ It is convenient to identify $G(r,n-r)$ with the space $\newcommand{\bR}{\mathbb{R}}$ $\Gr_r(\bR^n)$ of $r$-dimensional subspaces of $\bR^n$ via the map
$$
\Gr_r(\bR …
- 34.7k