On the existence of stable bundles with prescribed Chern classes on Calabi–Yau threefolds

We prove a case of the conjecture of Douglas, Reinbacher and Yau about the existence of stable vector bundles with prescribed Chern classes on a Calabi–Yau threefold. For this purpose we prove the existence of certain stable vector bundle extensions over elliptically fibered Calabi–Yau threefolds.