On Křížek’s decomposition of a polyhedron into convex components and its applications in the proof of a general Ostrogradskij’s theorem. (English) Zbl 1313.52015

Ženíšek, Alexander

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 2–5, 2012. In honor of the 60th birthday of Michal Křížek. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-60-8/pbk). 309-316 (2012).

The author reminisces about a result by M. Křížek from 1982 on the decomposition of an arbitrary polyhedron into finitely many convex polyhedra with disjoint interior. As a consequence he was able to provide a proof of the Ostrogradskij’s theorem in a simpler form than that was known at that time. The paper is mostly expository and written on the occasion of Křížek’s 60-th birthday, but contains references to the literature for those interested in the details.
For the entire collection see [Zbl 1277.00031].

Reviewer: Jan Brandts (Amsterdam)

MSC:

52B10	Three-dimensional polytopes
65N99	Numerical methods for partial differential equations, boundary value problems

Keywords:

polyhedron; convexity; Ostrogradskij’s theorem; surface integral; trace theorem