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The Copts, adherents of the Egyptian Orthodox Church, today represent the largest Christian community in the Middle East, and their presiding bishops have been accorded the title of pope since the third century AD. This study analyzes the development of the Egyptian papacy from its origins to the rise of Islam. How did the papal office in Egypt evolve as a social and religious institution during the first six and a half centuries AD? How do the developments in the Alexandrian patriarchate reflect larger developments in the Egyptian church as a whole—in its structures of authority and lines of communication, as well as in its social and religious practices? In addressing such questions, Ste...
The fascinating life of Frances Jennings, elder sister of Sarah, Duchess of Marlborough, charting her marriages and changes of fortune, her exile and return, her ambition, political manoeuvring and sincere piety.Frances Jennings, elder sister of Sarah, duchess of Marlborough, had an interesting and eventful life, most notably as the influential wife of Richard Talbot, earl of Tyrconnell, Catholic viceroy of Ireland under James II. Born circa 1649 into a Hertfordshire gentry family, she was a noted beauty at the Restoration court. There, she met and married George Hamilton, a Catholic officer who, after 1667, served in Louis XIV's army. In Paris, Frances raised three daughters, converted to C...
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Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.