Dr. Christian Scharrer

Postdoctoral assistant of Prof. Dr. Stefan Müller Room: 2.053 Email: Scharrer@iam.uni-bonn.de Phone: +(49)228-73-62298

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Research summary

I'm interested in geometric variational problems, as well as related inequalities, and gradient flows. My focus lies on the minimization of curvature based functionals in the class of immersed surfaces. This includes the Lebesgue 2-norm of the mean curvature, known as Willmore energy, or the so-called Helfrich functional, which models the energy of lipid bilayer cell membranes. I investigate how global constraints on area, volume, or total mean curvature can influence the shape of minimizers. Moreover, I explore the effects of small energy on geometry and topology. Together, my friends and I discovered a sharp energy threshold for the Willmore functional that excludes the existence of short closed geodesics. The methods that I use combine geometric measure theory, differential geometry, the theory of partial differential equations, and functional analysis.