Την Τετάρτη 11/12/2024 και ώρα 16:00 θα πραγματοποιηθεί διαδικτυακή ομιλία με τίτλο “On biharmonic and conformal biharmonic maps” και ομιλητή τον κ. Volker Branding (Faculty of Mathematics, University of Vienna).
Η ομιλία θα πραγματοποιηθεί μέσω της πλατφόρμας zoom στο σύνδεσμο https://zoom.us/my/uowm.math1.
Περίληψη Ομιλίας:
In the first part of the talk we will provide an introduction to both harmonic and biharmonic maps between Riemannian manifolds and present some of the key results on them that have been obtained over the years. Harmonic maps are represented by a nonlinear second order equation which arises as critical point of the energy of a map. Harmonic maps are special in two dimensions as in this case they are invariant under conformal transformations. Biharmonic maps, being critical points of the bienergy functional, constitute a nonlinear fourth order equation and are not conformally invariant in any dimension.
In the second part we will introduce a version of the bienergy functional that is conformally invariant on four-dimensional manifolds and whose critical points are called conformal biharmonic maps. We will present the basic properties of conformal biharmonic maps with particular attention to conformal biharmonic hypersurfaces in space forms and the stability of conformal biharmonic hyperspheres. Moreover, we will point out many surprising differences between biharmonic and conformal biharmonic maps.
This is joint work with Simona Nistor and Cezar Oniciuc.