Oberseminar Differentialgeometrie: Volker Branding (Universität Wien), Vortrag: On conformal biharmonic maps and hypersurfaces
Monday, 10.06.2024 16:00 im Raum Zoom
Abstract:
Biharmonic maps are a fourth order generalization of the well-studied harmonic map equation.
They can be characterized as critical points of the bienergy for maps between two Riemannian
manifolds. While the energy for maps, whose critical points are precisely harmonic maps, is
invariant under conformal transformations for a two-dimensional domain the bienergy is not
invariant under conformal transformations in any dimension.
In this talk we will introduce a version of the bienergy 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.
Angelegt am 04.06.2024 von Sandra Huppert
Geändert am 04.06.2024 von Sandra Huppert
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