0 , ▁there ▁exists ▁a ▁two - dimensional ▁Riemann ian ▁manifold ▁M ▁with ▁the ▁is oper imet ric ▁constant ▁h ( M ) ▁= ▁h ▁and ▁such ▁that ▁the ▁k th ▁eigen value ▁of ▁the ▁Lap la cian ▁is ▁within ▁ ε ▁from ▁the ▁Che eg er ▁bound ▁( B user , ▁ 1 9 7 8 ). ▁ ▁B user ' s ▁inequality ▁▁ ▁Peter ▁B user ▁proved ▁an ▁upper ▁bound ▁for ▁ ▁in ▁terms ▁of ▁the ▁is oper imet ric ▁constant ▁h ( M ). ▁Let ▁M ▁be ▁an ▁n - dimensional ▁closed ▁Riemann ian ▁manifold ▁whose ▁Ric ci ▁curv ature ▁is ▁bounded ▁below ▁by ▁− ( n − 1 ) a 2 , ▁where ▁a ▁ ≥ ▁ 0 . ▁Then ▁ ▁See ▁also ▁▁▁ ▁Che eg er ▁constant ▁( graph ▁theory ) ▁ ▁Is oper imet ric ▁problem ▁ ▁References ▁▁▁▁▁▁▁▁▁▁▁▁ ▁Category : R iemann ian ▁geometry <0x0A> </s> ▁The ▁women ' s ▁ 8 0 0 ▁metres ▁event ▁at ▁the ▁ 2 0 1 1 ▁Summer ▁Univers ia de ▁was ▁held ▁on ▁ 1 6 – 1 8 ▁August . ▁ ▁Medal ists ▁ ▁Results ▁ ▁He ats ▁Qual ification : ▁First ▁ 3 ▁in ▁each ▁heat ▁( Q ) ▁and ▁the ▁next ▁ 4 ▁fast est ▁( q ) ▁qualified ▁for ▁the ▁semif inals . ▁ ▁Sem if inals ▁Qual ification : ▁First ▁ 3 ▁in ▁each ▁heat ▁( Q ) ▁and ▁the ▁next ▁ 2 ▁fast est ▁( q ) ▁qualified ▁for ▁the ▁final . ▁