On the second part of Hilbert's fifth problem.
The addition formula for theta functions.
The addition formula for theta functions. (Summary).
The addition theorem of Weierstrass' s sigma function.
Smooth quasiregular mappings with branching
We give an example of a -smooth quasiregular mapping in 3-space with nonempty branch set. Moreover, we show that the branch set of an arbitrary quasiregular mapping in-space has Hausdorff dimension quantitatively bounded away from . By using the second result, we establish a new, qualitatively sharp relation between smoothness and branching.
Quasiconformal mappings with Sobolev boundary values
We consider quasiconformal mappings in the upper half space of , , whose almost everywhere defined trace in has distributional differential in . We give both geometric and analytic characterizations for this possibility, resembling the situation in the classical Hardy space . More generally, we consider certain positive functions defined on , called conformal densities. These densities mimic the averaged derivatives of quasiconformal mappings, and we prove analogous trace theorems for them....
Metric distorsion and triangle maps.
Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary.
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