Event

Talk
Singularities of Minimal Surfaces and Harmonic Maps
Leon Simon (guest of the AEI)
6 Dec 2005, 15:00 – 16:00

In the latter half of the 20'th century much was achieved in understanding regularity properties of minimal surfaces and harmonic maps, and major theorems were proved, for example in the direction of limiting the dimensional size of the singular set for various sub-classes of such surfaces and maps. In particular various "partial regularity theories'' based on ideas of De Giorgi, Reifenberg, Federer, Almgren and others were developed. Nevertheless many very basic questions about the nature of the singular set have remained completely open; for example, does the singular set have some sort of stratified structure analogous to the stratification of the singular part of general real analytic varieties. This talk will briefly survey the present state of knowledge and conclude with a discussion of recent work which aims to develop a framework for a special class of singular minimal surfaces which is on the one hand analytically manageable and on the other hand sufficiently rich in examples to provide insights into the general situation alluded to above.