Contractible 3-manifolds and positive scalar curvature

It is known that \(\mathbb{R}^3\) admits a complete metric of uniformly positive scalar curvature. In fact, for any closed manifold \(X\) and any \(k \ge 3\) the manifold \(X \times \mathbb{R}^k\) admits a complete metric of uniformly positive scalar curvature by a result of Rosenberg and Stolz (link). Now there exist contractible, open 3-manifolds which are not … Continue reading "Contractible 3-manifolds and positive scalar curvature"

Prizes, prizes, prizes

Several prizes have been awarded in the past few weeks to mathematicians. Kyoto Prize The Kyoto Prize 2018 in the category Basic Sciences was awarded to Masaki Kashiwara from the RIMS at Kyoto University. (announcement) The Kyoto Prize is awarded annually to “those who have contributed significantly to the scientific, cultural, and spiritual betterment of mankind” … Continue reading "Prizes, prizes, prizes"

Two new presidents

Professor Volker Mehrmann from the TU Berlin was elected as the new president of the European Mathematical Society (EMS). His four-year term will start January 1st, 2019. More information can be found in the press release: link. Professor Daya Reddy was elected first president of the International Science Council (ISC). The ISC is newly founded … Continue reading "Two new presidents"

Stable minimal surfaces in 3-manifolds

Meeks-Pérez-Ros conjectured in their article “Stable constant mean curvature surfaces” (2008) the following: if a closed, connected Riemannian 3-manifold N does not admit any closed, embedded minimal surfaces whose two-sided covering is stable, then N is finitely covered by the 3-sphere. Recall that a surface is called minimal if it is a critical point of … Continue reading "Stable minimal surfaces in 3-manifolds"

Manfredo do Carmo 1928-2018

Manfredo do Carmo was a Brazilian mathematician working in differential geometry. 1978 he was an invited speaker at the ICM in Helsinki, and 1971-1973 he was president of the Brazilian Mathematical Society. Besides for his mathematical research he was also known for his textbooks.

Mathematik in der Blütezeit des Islam

Die Wikipedia veranstaltet jährlich einen Schreibwettbewerb (link). Es gibt jeweils einen Jurypreis und einen Publikumspreis, und dieses Jahr ging der Publikumspreis an einen mathematischen Artikel: Mathematik in der Blütezeit des Islam. Ein paar mehr Infos gibt es auch in diesem ScienceBlog: link.