Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean   space
  Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a restricted class of topologies is consistent with the metric and the dilaton. A particular case of string motivated Liouville gravity is studied in detail. Path integral quantisation in generic Euclidean dilaton gravity is performed non-perturbatively by analogy to the Minkowskian case. 
L. Bergamin (Vienna, Tech. U.), D. Grumiller (Leipzig U.), W. Kummer   (Vienna, Tech. U.), D.V. Vassilevich (Leipzig U.)