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I have a general question in Riemannian geometry: Let M be a compact manifold and $\partial M \neq \emptyset$. Then shoot a geodesic from any boundary point perpendicularly into the interior of M. How …

I read a paper saying the Mobius transformation from $\mathbb{R}^n\cup \infty \to \mathbb{R}^n\cup \infty$is generated by translations, scalar multiplications and inversions $x\to \frac{x}{|x|^2}$. So …

I like the presentation from Analytic methods in algebraic geometry by Demailly. Here is the link: http://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/eem2007.pdf.

Another thing needs to mention is cscK on a polarized K\"{a}hler manifolds whose existence is conjectured to be equivalent to a notion of stability. See the work of Donaldson, Tian, et al.

Are there examples of Kähler manifolds whose Kähler cone can be described explicitly, say spanned by certain cohomology classes? As far as I know, Hirzebruch Surface has a complete description for it …