Constant Mean Curvature Surfaces and Smoke Ring Flow

• Applicant: Professor Dr. Ulrich Pinkall
• Subject Area: Mathematics
• Term: from 2010 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 179877155

• Final Report Year: 2014

Final Report Abstract

We obtained many exciting new results concerning surfaces with prescribed mean curvature half density and other classes of submanifolds. These results were partially based on a lively research network (which we inherited from previous projects) between geometers at TU Berlin and colleagues in China and Eastern Europe.

Publications

• Conformal deformations of immersed discs in R3 and elliptic boundary value problems
  C. Bohle and U. Pinkall
  
• Curvature properties of Weyl geometries, Results Math. 59 (2011), 523-544
  P. Gilkey and St. Nikcevic and U. Simon
  
• Geometric modelling techniques for the solution of certain Monge- Ampère equations, in: Advanced Lectures in Mathematics, Volume 21, Advances of Geometric Analysis (2011), 19-42
  U. Simon and R. Xu
  
• Geometric realizations, curvature decompositions and Weyl manifolds, J. Geometry and Physics 61 (2011), 270-27
  P. Gilkey and St. Nikcevic and U. Simon
  
• Notes on Chern’s Affine Bernstein Conjecture, Results Math. 60 (2011), 133-155
  A.M. Li, R. Xu and U. Simon and F. Jia
  
• Shiing-Shen Chern’s 100th birthday, Results in Mathematics, 60 (2011), 13-51
  U. Simon and E-H. Tjaden and H. Wefelscheid
  
• Parallel hypersurfaces, Annales Polonicí Mathematici, 2014 > 111 > 2 > 107-135. journal ISSN : 0066-2216
  Barbara Opozda, Udo Simon
  (See online at https://doi.org/10.4064/ap111-2-1)
• Global Affine Differential Geometry of Hypersurfaces, Walter de Gruyter GmbH & Co KG, 17.08.2015 - 376 S. … second edition of this monograph
  An-Min Li, Udo Simon, Guosong Zhao, Zejun Hu