Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
We give rigidity results for discrete Bonnet-Myers diameter bound and Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if the underlying graph is a hypercube. The proofs use well-known semigoup methods as well as new direct methods which translate curvature to combinatorial properties. The results can be seen as first known discrete analogues of Cheng's and Obata's rigidity theorems.