The classification of simple singularities of nondegenerate functions on Legendrian submanifolds of contact manifolds up to Legendrian equivalences was found. New singularities of Lagrangian manifolds arrising in the obstacle problem were found. The classification of simple singularities of Lagrangian manifolds arrising in symplectic reduction was found in a joint paper with V. M. Zakalyukin.
Main publications:
Myasnichenko O. M. Osobennosti volnovykh frontov na granitse razdela dvukh sred // Algebra i analiz, 1993, t. 5, # 4.
Myasnichenko O. M. Pryamoe proizvedenie raskrytykh lastochkinykh khvostov v zadache ob obkhode prepyatstviya // Funkts. analiz i ego prilozheniya, 1996, t. 30, # 4.
Zakalyukin V. M., Myasnichenko O. M. Lagranzhevy osobennosti pri simplekticheskoi reduktsii // Funkts. analiz i ego prilozheniya, 1998, t. 32, # 1.
