0
votes
0answers
68 views

Existence of special pants decompositions for non-elementary representations into PSL(2,R)

A Theorem by Gallo, Goldman and Porter states the following: Let $S_g$ be a closed orientable surface of genus $g$ with fundamental group $\Gamma_g$, and fix a non-elementary representation ...
12
votes
2answers
476 views

On closed simple curve with curvature at most 1

I am looking for the reference to the following theorem. I have to apply a similar statement, and it would be nice to trace the source. Please note, I know few proofs in fact it is Problem 3 in my ...
3
votes
2answers
380 views

Surfaces in $\mathbb R^3$ with negative curvature bounded away from zero

Is there a surface in $\mathbb R^3$ which is a closed subset and whose curvature is negative and bounded away from zero? And the small-print... By surface I mean smooth surface without ...
1
vote
2answers
235 views

Numerically negative exceptional divisor on a surface.

Suppose $S$ is an algebraic surface (possibly projective) over an algebraically closed field $k$. Suppose $D_i$ are irreducible smooth curves (rational, if you want) with negative self-intersection ...
0
votes
2answers
1k views

Parametrization of the intersection of an ellipsoid with a sphere

Hi, Fisrt I would like to say that geometry is far away from my domain. I have encountered a problem that has a geometric formulation and I don't even know if this is a difficult or an easy ...