Richard Bulliet 's "conversion curve" shows a relatively low rate of conversion of non-Arab subjects during the Arab centric Umayyad period of 10%, in contrast with estimates for the more politically multicultural Abbasid period which saw the Muslim population grow from approx. 40% in the mid-9th century to close to 100% by the end of the 11th century.  This theory does not explain the continuing existence of large minorities of Christians in the Abbasid Period. Other estimates suggest that Muslims were not a majority in Egypt until the mid-10th century and in the Fertile Crescent until 1100. Syria may have had a Christian majority within its modern borders until the Mongol Invasions of the 13th century.
Between 1354 (when the Ottomans crossed into Europe at Gallipoli) and 1526, the Empire had conquered the territory of present-day Greece, Bulgaria, Romania, Albania, Serbia, Macedonia, Montenegro, Bosnia, and Hungary. The Empire laid siege to Vienna in 1683. The intervention of the Polish King broke the siege, and from then afterwards the Ottomans battled the Habsburg Emperors until 1699, when the Treaty of Karlowitz forced them to surrender Hungary and portions of present-day Croatia, Slovenia, and Serbia. From 1699 to 1913, wars and insurrections pushed the Ottoman Empire further back until it reached the current European border of present-day Turkey.