Partielle Differentialgleichungen

Abstract

\noindent The workshop \emph{Partial differential equations}, organised by Tom Ilmanen (ETH Z\"urich), Reiner Sch\"atzle (Universit\"at T\"ubingen) and Neil Trudinger (Australian National University Canberra) was held July 24-30, 2005. This meeting was well attended by 46 participants, including 6 females, with broad geographic reprensentation. The program consisted of 15 talks and 9 shorter contributions and left sufficient time for discussions. \medskip \noindent New results combining partial differential equations and geometric problems were presented in the area of minimal surfaces, free boundaries and singular limits, for example the construction of branched minimal surfaces, the regularity of free boundaries in the wake of the monotonicity formula of Weiss and a proof of a conjecture of De Giorgi. \medskip \noindent A major part of the leading experts of partial differential equations with conformal invariance attended the workshop. Here new results were presented in conformal geometry, for the Yamabe problem, the Paneitz operator and the Willmore functional.