In the previous set of notes we introduced the notion of a *complex diffeomorphism* between two open subsets of the complex plane (or more generally, two Riemann surfaces): an invertible holomorphic map whose inverse was also holomorphic. 13,203 more words

## Tags » Math.DG

#### 246A, Notes 5: conformal mapping

#### Math 246A, Notes 4: singularities of holomorphic functions

In the previous set of notes we saw that functions that were holomorphic on an open set enjoyed a large number of useful properties, particularly if the domain was simply connected. 11,793 more words

#### Notes on the Nash embedding theorem

Throughout this post we shall always work in the smooth category, thus all manifolds, maps, coordinate charts, and functions are assumed to be smooth unless explicitly stated otherwise. 2,833 more words

#### Harmonic quasi-isometries (after Benoist and Hulin)

Last September 28, Yves Benoist gave a beautiful talk on the occasion of the workshop Geometry and Dynamics on Moduli Spaces (that is, one of the four… 2,063 more words