I study geometric and topological features of  bending energies and their applications. These energies appear, for instance, in the Canham-Helfrich model in cellular biology which can be used to describe the shape of red blood cells. Another important example is Euler's elastic energy in elasticity theory.

Related publications: [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]

Points of higher multiplicity can be the source for singularities in geometric analysis. I am interested in finding energy levels that prevent points of higher multiplicity (or, more generally, the formation of singularities) for geometric curvature functionals.

Related publications: [4], [6], [7], [9], [12]

I work on extrinsic geometric flows for curvature functionals with constraints, focusing on global existence, formation of singularities, asymptotic behavior and qualtitative properties.

Related publications: [1], [2], [3], [5], [6], [8], [11], [13], [15]

I am interested in finding sufficient conditions for these functional analytic inequalities, which then provide fundamental tools for the asymptotic analysis of the associated gradient flows. 

Related publications: [1], [2], [3], [5], [8], [13]