The derivative in a certain direction is the angular coefficient of the corresponding generator of the tangent cone. In a plane section of the surface z = f(x, y) we get a curve that is the difference of convex curves. This is just an analytical expression of the fact that the intersection of convex sets is convex.
The convergence of the series Pgi(x) at at least one point is a necessary and sufficient condition for f(x) to be the difference of convex functions. If for a surface F the slopes of the tangent semi-axes (derivatives in each direction) are at most several M, then the distance ρF between the points .
СИБИРСКИЕ ЭЛЕКТРОННЫЕ МАТЕМАТИЧЕСКИЕ ИЗВЕСТИЯ
ALEXANDROV IN 1945
At the physics faculty, where he graduated in 1932, his supervisor in physics was the outstanding physicist-theorist V. Cohn-Vossen, a German refugee and a student of Hilbert who used visual methods in the theory of geodesics on surfaces. This book was published in German in 1934 and briefly summarized the results of D's Geometric school.
The Leningrad Department of the Steklov Mathematical Institute (LDMI) was founded in 1940, and A.D., then a doctor of physics and mathematics since 1937, became one of its first researchers. In particular, he proved that such a surface almost everywhere has a second differential and developed a general theory of additive functions of a set. He proposed a visual-geometric approach to a series of problems and solved some of the most difficult questions of the theory of convex polyhedra and convex surfaces.
In this process, the properties of the concepts and their possible generalizations were discussed in depth and problems were suggested. These years, second to fourth year students attended many seminars choosing a suitable program or topic for their Master's thesis. An atmosphere of equality of all speakers in front of the scientific truth was created, regardless of their ranks.
Unlike many modern seminars (let alone conferences) where only the final results are reported while the evidence is presented very briefly, in this seminar one could also discuss projects and different approaches to problems. In this process he told as a joke how his teacher, Delone, maintained the colossal importance of each successive problem; but when A.D. Friendly peer editing of publications by young participants in the seminar was also a common practice.
ALEKSEY VASIL’EVICH POGORELOV (1919–2002)
YURI GRIGORIEVICH RESHETNYAK
YURI ALEXANDROVICH VOLKOV (1930–1981)
Rokhlin created the most coordinated curriculum between all departments. However, for the reasons of "simplification" this plan only lasted for two years.). He also solved a Cohn-Vossen problem and obtained an estimate of the spatial deformation of a closed convex surface in terms of deformation of its intrinsic metric. He ably helped them to develop their knowledge, talking with them for hours in the evenings at his home.
Here is a possibly incomplete list of his former graduate students (all who visited A.D.'s seminary): Mekhtiev, an assistant professor in Makhachkala;. Dexter, professor in Canada; Kagan was an assistant professor at Southwestern Polytechnic Institute; Podgornova, assistant professor in Tashkent; Al-Etrebi (Saudi Arabia); Abu Dhabi (Egypt); Nevmerzhitski works in St. Lifshits died in a car accident in 1976; Alekseeva, assistant professor at the Academy of Wood Industry; Kishukov, assistant professor at Nalchik, Alexandrova; and Brumberg.
IL’YA YAKOVLEVICH BAKEL’MAN (1928–1992)
On the path that many geometers dream of, he proved the existence of a convex polyhedron with a given development by constructing in an abstract class of objects an extreme problem for which the extremum exists by compactness and the extreme object is the desired polyhedron. He had many postgraduate students who held numerous positions in pedagogical institutes of different cities. Bakel'man keenly felt a number of personal limitations that were increasing in Russia at that time.
He was denied membership of the Communist Party of the USSR (hereinafter abbreviated as Party or CPSU). In 1973 he was forced to resign as head of the Geometry department he founded. He then wanted to move to the Petrozavodsk Pedagogical Institute, but the government there also rejected him.
In the USA, he held a professorship at Texas A&M University, communicated with leading mathematicians and participated in many international conferences.
YURI FEDOROVICH BORISOV (1925–2007)
VIKTOR ABRAMOVICH ZALGALLER
This was one of the first works where computer calculations were the basis of a theoretical proof. Burago and papers on convex bodies, taught at LSU as a professor and worked at LDMI/PDMI until 2000 (when I retired at age 79). My postgraduate students were: Burago (head of PDMI's geometry department), Stratilatova (died early), Fedotov (an associate professor at the Academy of Agriculture), Trushina, Makeev (an associate professor at SPSU's Geometry Department—St. Petersburg State University), and Kozlov (Doctor of Sciences , a lecturer at SPSU's Geometry Department).
REVOLT IVANOVICH PIMENOV (1931–1990)
In early 1990, Pimenov was elected a member of the Supreme Soviet of the Russian Federation from Komi. Until his death (he died of stomach cancer at the end of 1990), he worked actively in Moscow in a committee on the new state constitution.
ALEXANDR MIKHAJLOVICH ZAMORZAEV–ORLEANSKIJ (1927–1997)
YURI EVELEVICH BOROVSKIJ
YURI DMITRIEVICH BURAGO
Pimenov was fully exonerated posthumously in 1991. associate professor at the Institute of Finance and Economics); Mostovskii (in Arkhangelsk); Perel0man (formerly at PDMI, now independent); and Petrunin (in the USA).
ALEKSEI LEONIDOVICH VERNER
A.D.’S POSTGRADUATE STUDENTS FROM OTHER CITIES BY 1963
Once Tartakovskii told me: "You break the commandment: 'Thou shalt not make any graven image.'" I still have a photo of a group of seminar participants taken by Pogorelov in 1955. This is just the school of hell run by the CONFERENCE AND OF SEMINAR GUESTS They were held almost every year and attracted many seminar participants and other mathematicians.
In 1956, during III. of the All-Union Mathematical Congress, among the guests of the seminar was the outstanding German geometer W. Busemann, who arrived at the IV. All-Federal Mathematical Congress; he was also a guest of the seminar. Verbitskaya (rector of SPBU from 1994 to 2008) attended the funeral of A.D. said that he had 4 orders of the Labor Red Banner and also 4 reprimands from party authorities (equaling them with decorations).
For them the university is buildings, but for me it is professors." Despite recommendations from the Leningrad City Committee, he invited some professors from the Academy, other institutes and other cities to university positions. He invented the morality of communist society, but we are still far from it.”. Between the University and the Sjezdovskaya line there is a large block of buildings of the Military Academy of the Rear and Transport.
The army was subject to a downsizing at the time and the academy had to move out of town. Excellent classrooms are empty in the second half of the day: seminars have chosen to meet in Leningrad. Uniqueness theorems for surfaces at large" and "Research on the maximum principle." There were also a few papers on isometric deformations and an article in German "On a generalization of Riemannian geometry." The latter became the basis for the theory of Alexandrov spaces, now studied by many geometers all over the world.
EPISODES OF FIGHT FOR GENETICS
Once in the fall, when I was visiting A.D., I told him how I was waiting for the train to Leningrad after a lecture on a very windy day. The latter became the basis of the theory of Alexander spaces, which is studied today by many geometers around the world. When he once commented on education, he told his students: “Personal example is an important tool of education.
Let me tell two stories: about A.D. 's fight for genetics and about the fate of a scientific school created because of A.D. 's support. When Khrushchev organized a meeting of the most active members of the Party in Leningrad that emphasized collective leadership, A.D. He was liberated by our army and then worked as an interpreter in the army headquarters.
After the war, he was sent to a detention camp for an "examination", where he was made not a detainee but a guard. In 1946 he was sent to Moscow where he worked in the LDMI and was a guide to (blind) Academician L. This brilliant scientist working in the rapidly developing Differential Topology and Ergodic Theory attracted gifted students and young faculties attracted.
Gromov, who worked in RIMM, then left and refused to work in Syktyvkar and emigrated. He leads a department in the USA and remains a member of the scientific council of PDMI, where he once led a department.
GROWTH OF THE UNIVERSITY
PHILOSOPHICAL VIEWS OF A.D
This can mean - being above "two camps" and talking to the core.
DEPARTURE TO NOVOSIBIRSK
I welcome all participants of the conference and hope that the meeting will be fully successful. This is the centenary of the birth of Alexander Danilovich Aleksandrov, who was an outstanding mathematician and a brilliant and attractive person. He had a unique understanding of life, he had a far-sighted vision of the universe, and he enjoyed a quality that in the slang of the recent totalitarian past was described as an inactive attitude towards life.
Professor Dmitri˘ı Konstantinovich Faddeev organized a problem-solving competition among the first and second year students of the Department of Mathematics and Mechanics. The problem statement was supplemented with the comment that the solution to the problem was unknown. Yusupov gave a proof of one theorem of the curve theory during one of the meetings of the seminary in the spring semester of 1949.
The result of the exam did not influence the amount of the scholarship, but if you got a C, then the re-exam was mandatory. I reveal that the first question in the exam was about the content of the only philosophy lecture for postgraduate students that I attended. By the way, the miracles in Father Aleksandr's sense, but with the opposite sign, happened to me many times.
He was elected to a vacant seat of a corresponding member of the Academy of Sciences of the USSR in 1946. In 1964 he was elected a full member of the Academy of Sciences and moved to Novosibirsk where he worked at the Institute of Mathematics (now the Sobolev Institute) and Novosibirsk State University. It was for this research that he was awarded the Stalin Prize of the second degree in 1942.
