A5071990021- Geometric Analysis and Curvature Flows
- Geometry and complex manifolds
- Analytic and geometric function theory
- Point processes and geometric inequalities
- Advanced Mathematical Modeling in Engineering
- Geometric and Algebraic Topology
- Computational Geometry and Mesh Generation
- Graph theory and applications
- Advanced Numerical Analysis Techniques
- Mathematics and Applications
- Nonlinear Partial Differential Equations
- Algebraic Geometry and Number Theory
- 3D Shape Modeling and Analysis
- Composite Material Mechanics
- Advanced Graph Theory Research
- Graph Labeling and Dimension Problems
- Quasicrystal Structures and Properties
- Spectroscopy and Quantum Chemical Studies
- Advanced Materials and Mechanics
- Lipid Membrane Structure and Behavior
- Photonic Crystals and Applications
- Photonic and Optical Devices
- VLSI and FPGA Design Techniques
- History and Theory of Mathematics
- Metamaterials and Metasurfaces Applications
Technical University of Darmstadt
2005-2023
University of Bonn
1992-2000
University of Illinois Urbana-Champaign
2000
University of Massachusetts Amherst
2000
Nature provides impressive examples of chiral photonic crystals, with the notable example cubic so-called srs network (the label for degree-three modeled on $\mathrm{SrS}{\mathrm{i}}_{2}$) or gyroid structure realized in wing scales several butterfly species. By a circular polarization analysis band such networks, we demonstrate strong dichroism effects: The microstructure, $I{4}_{1}32$ symmetry, shows significant blue to ultraviolet light, that warrants search biological receptors sensitive...
We want to summarize some established results on periodic surfaces which are minimal or have constant mean curvature, along with recent results. will do this from a mathematical point of view general readership in mind.
Inverse bicontinuous cubic phases with two aqueous network domains separated by a smooth bilayer are firmly established as equilibrium in lipid/water systems. The purpose of this article is to highlight the generalisations these geometries polycontinuous geometries, which could be realised lipid mesophases three or more network-like branched bilayer. An analysis structural homogeneity terms width variations reveals that ordered likely candidates for mesophase structures, similar chain...
We use Brakke's Surface Evolver to deform a triply periodic minimal surface, the gyroid, into continuous family of constant mean curvature surfaces with same symmetry. discuss stability and bifurcation problems for these surfaces.
Article Triunduloids: embedded constant mean curvature surfaces with three ends and genus zero was published on November 12, 2003 in the journal Journal für die reine und angewandte Mathematik (volume 2003, issue 564).
We consider constant mean curvature surfaces with finite topology, properly embedded in three-space the sense of Alexandrov.Such three ends and genus zero were constructed completely classified by authors.Here we extend arguments to case an arbitrary number ends, under assumption that asymptotic axes lie a common plane: construct classify entire family these genus-zero, coplanar surfaces. Dedicated Hermann Karcheron occasion his 65th birthday.
We announce the classification of complete almost embedded surfaces constant mean curvature, with three ends and genus zero. They are classified by triples points on sphere whose distances asymptotic necksizes ends.
Abstract We study a problem of geometric graph theory: determine the triply periodic in Euclidean 3-space which minimizes length among all graphs spanning fundamental domain with same volume. The minimizer is so-called network quotient complete on four vertices $$K_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>K</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> . For comparison we consider competing topological class, also vertices, and minimizing networks.
We prove each embedded, constant mean curvature (CMC) surface in Euclidean space with genus zero and finitely many coplanar ends is nondegenerate: there no nontrivial square-integrable solution to the Jacobi equation, linearization of CMC condition. This implies that moduli such surfaces a real-analytic manifold neighborhood these full itself manifold. Nondegeneracy further (infinitesimal local) rigidity sense asymptotes map an analytic immersion on spaces, also classifying diffeomorphism.
We consider constant mean curvature surfaces of finite topology, properly embedded in three-space the sense Alexandrov. Such with three ends and genus zero were constructed completely classified by authors arXiv:math.DG/0102183. Here we extend arguments to case an arbitrary number ends, under assumption that asymptotic axes lie a common plane: construct classify entire family these genus-zero coplanar surfaces.
In 1841, Delaunay constructed the embedded surfaces of revolution with constant mean curvature (CMC); these unduloids have genus zero and are now known to be only CMC two ends finite genus. Here, we construct complete family three zero; they classified using their asymptotic necksizes. We work in a class slightly more general than surfaces, namely immersed which bound an three-manifold, as introduced by Alexandrov.
We prove each embedded, constant mean curvature (CMC) surface in Euclidean space with genus zero and finitely many coplanar ends is nondegenerate: there no nontrivial square-integrable solution to the Jacobi equation, linearization of CMC condition. This implies that moduli such surfaces a real-analytic manifold neighborhood these full itself manifold. Nondegeneracy further (infinitesimal local) rigidity sense asymptotes map an analytic immersion on spaces, also classifying diffeomorphism.