Zusammenfassung
Let M be a compact manifold with a metric g and with a fixed spin structure chi. Let lambda(+)(1) be the first non-negative eigenvalue of the Dirac operator on (M, g, chi). We set tau(M, chi) := sup inf lambda(+)(1)(g) where the infimum runs over all metrics g of volume 1 in a conformal class [g(0)] on M and where the supremum runs over all conformal classes [g(0)] on M. Let (M-#, chi(#)) be ...
Zusammenfassung
Let M be a compact manifold with a metric g and with a fixed spin structure chi. Let lambda(+)(1) be the first non-negative eigenvalue of the Dirac operator on (M, g, chi). We set tau(M, chi) := sup inf lambda(+)(1)(g) where the infimum runs over all metrics g of volume 1 in a conformal class [g(0)] on M and where the supremum runs over all conformal classes [g(0)] on M. Let (M-#, chi(#)) be obtained from (M, chi) by 0-dimensional surgery. We prove that tau(MK#, chi(#)) >= tau(M, chi). As a corollary we can calculate tau(M, chi) for any Riemann surface M.
Altmetric