Löwner-john Ellipsoids

Before giving the mathematical description of the Löwner-John ellipsoids and pointing out some of their far-ranging applications, I briefly illuminate the adventurous life of the two eminent mathematicians, by whom the ellipsoids are named: Charles Loewner (Karel Löwner) and Fritz John. Karel Löwner was born into a Jewish family in Lány, a small town about 30 km west of Prague, in 1893. Due to his father’s liking for German style education, Karel attended a German Gymnasium in Prague and in 1912 he began his studies at German Charles-Ferdinand University in Prague, where he not only studied mathematics, but also physics, astronomy, chemistry and meteorology. He made his Ph.D. in 1917 under supervision of Georg Pick on a distortion theorem for a class of holomorphic functions. In 1922 he moved to the University of Berlin, where he made his Habilitation in 1923 on the solution of a special case of the famous Bieberbach conjecture. In 1928 he was appointed as non-permanent extraordinary professor at Cologne, and in 1930 he moved back to Prague where he became first an extraordinary professor and then a full professor at the German University in Prague in 1934. After the complete occupation of Czech lands in 1939 by Nazi Germany, Löwner was forced to leave his homeland with his family and emigrated to the United States. From this point on he changed his name to Charles Loewner. He worked for a couple of years at Louisville, Brown and Syracuse University, and in 1951 he moved to Stanford University. He died in Stanford in 1968 at the age of 75. Among the main research interests of Loewner were geometric function theory, fluid dynamics, partial di↵erential equations and semigroups. Robert Finn (Stanford) wrote about Loewner’s scientific work: “Loewners Verö↵entlichungen sind nach heutigen Maßstäben zwar nicht zahlreich, aber jede für sich richtungsweisend.”