# Robert Gulliver

## In Memoriam

We are all very shocked by the sad news that our long time colleague, Bob Gulliver, passed away on October 15, 2017.

Bob was born in the city of Torrance, California, on July 24, 1945. He started out his undergraduate career at Stanford aiming at a degree in physics, not mathematics. However, he switched to a math major during his junior year and continued on to obtain his math Ph. D. degree. As a graduate student at Stanford Bob worked first with Hans Samelson in algebraic topology, but found the machinery of that subject less inviting than differential geometry and variational problems. He worked for a time with Robert Finn, and then wrote a thesis with Robert Osserman, on branch points of surfaces with constant mean curvature. Osserman had recently proved a major theorem in this area, disproving assertions of Jesse Douglas and Richard Courant. This sparked Bob's interest, and led to his continued research on related problems.

Bob’s research work has spanned a wide range of topics related to differential geometry, partial differential equations and the calculus of variations. He has made extensive and important contributions to the study of minimal surfaces. One of his most well known results concerns the regularity of the resulting minimal (or more generally constant mean curvature) surfaces for Plateau’s problem in arbitrary three manifolds.

After his PhD, Bob was an instructor at U.C. Berkeley during 1971-73, which, not surprisingly, he found to be a stimulating environment. In particular he enjoyed having an office close to those of Ed Spanier and Shiing-Shen Chern. Chern was one of the most prominent figures in twentieth century differential geometry, and had many graduate students. Once or twice a week Bob would see a long line of graduate students outside Chern's office, each waiting for their turn for a few minutes of wisdom. After Berkeley, Bob came to Minnesota in 1973. Minnesota had many people that he could interact with, including Johannes Nitsche in minimal surfaces, Jim Serrin, Hans Weinberger, Walter Littman and others working in partial differential equations, as well as David Kinderlehrer and Robert Hardt in calculus of variations and Leon Green and Bill Pohl in differential geometry. Bob also made the best of Minnesota's weather by taking up cross-country skiing after his arrival here. Living near Kenwood park meant he could do some skiing without going very far.

Bob has had many collaborations throughout his career with mathematicians around the world, including several colleagues at Minnesota. Stimulated by comments of Leon Green, he wrote a paper in 1975 on manifolds without conjugate points, which led to considerable research by others, as well as a joint paper with Leon in 1984. Much later Bob collaborated with Walter Littman and others in a series of papers on control theory. Bob’s interests were quite broad. Fadil Santosa and his student Jing Wang approached him about a problem arising in multi-focal lens design. He ended up co-advising Jing on his thesis. This work led to a US patent that the University successfully licensed to a lens manufacturer. Bob served twice as Associate Director at the Institute for Mathematics and its Applications (1994-98 and 2001-2002), and was very engaged in the scientific life of the institute.

Bob has had seven PhD students, and has held many visiting positions over the years, including Germany, particularly at the University of Bonn, as well as in Italy and Australia. While at Bonn, Bob had an extensive collaboration with Stefan Hildebrandt, which inspired a number of Hildebrandt's students to make advances on problems raised in Bob's research. In addition to his many visits and visiting positions abroad, Bob has also organized many international conferences including the Yamabe Memorial Symposiums here. He was also the joint editor of two books.

Bob is well respected in the research community. In recognition of his contributions, a conference on "Calculus of Variations and Nonlinear Partial Differential Equations", was held in Hangzhou, China in 2005, jointly in honor of the sixtieth birthdays of Bob, Robert Hardt, and Leon Simon. Bob was not able to attend the conference, unfortunately, since he was the victim of a hit and run accident shortly before the conference, while riding his bicycle. Luckily Bob recovered well, and was able to get back to riding his bike vigorously!

Bob is survived by wife of 31 years, Kathryn "Kacy", son Jacob Gulliver, and brother John Gulliver, a professor in the Department of Civil, Environmental, and Geo-Engineering here at the University of Minnesota. He spent his career joyfully teaching mathematics at the University of Minnesota. He enjoyed being a father and family man, traveling, and had a life-long love of choral music. He will be sorely missed.