2014 Stanisław Łojasiewicz Lecture

Preparatory Workshop

Kraków, 28 May 2014 (Wednesday)


Barbara Opozda (UJ) A short introduction to the geometry of surfaces I

Abstract: Basic notions (in particular curvatures) for surfaces in 3-dim. Riemannian manifolds will be introduced. Minimality will be discussed, including few characterizations, few examples and variational formulas. The Jacobi operator and the Morse index will be defined.


coffee break


Barbara Opozda (UJ) A short introduction to the geometry of surfaces II


Paweł Strzelecki (University of Warsaw) Analytic aspects of Willmore surfaces

Abstract: We shall introduce the Willmore functional and present a self-contained survey of existence results (of Simon, Bauer and Kuwert, and others) for minimizers of prescribed genus. The main difficulties of the existence proofs will be sketched.


Lunch break


Paweł Walczak (University of Łódź) Existence and classication of foliations by surfaces of given conformal geometry

Abstract: It is known that (1) locally, around a non-umbilical point, conformal geometry of a surface in a constantly curved 3-manifold is completely determined by ve local conformal invariants (LCI's): three scalar and two vectorial quantities, (2) all the closed 3-manifolds admit foliations of codimension 1. Here, we will discuss the problem of existence and classication of foliations of closed constantly curved 3-manifolds by leaves belonging to particular classes of surfaces dtermined by their LCI's: those with either vanishing or constant scalar LCI's, canal surfaces etc. The presentation will be based on results obtained jointly with Adam Bartoszek, Gilbert Hector, Remi Langevin and Szymon Walczak during the last decade.


Sławomir Dinew (UJ) Yamabe problem

Abstract: We shall briefly introduce the Yamabe problem, and the historical developments leading to its solution. We shall focuss on the compactness issues of the approximating sequences of solutions, and the recent spectacular examples of Brendle and Brendle-Marques of noncompactness in high dimensions.

All lectures will take place in Room 1016 of the Department of Mathematics and Computer Science of Jagiellonian University (New Campus, Kraków).

Please contact Zbigniew Błocki for further details.