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401-3830-22L 4 Credits BSC , MSC D-MATH

Seminar on Minimal Surfaces (an Invitation to Geometric Analysis)

Lecturers & Examiners: Dr. Alessandro Carlotto
The total number of students who may take this course for credit is limited to twenty; however further students are welcome to attend.
VVZ CR n/a

Last Updated: 2026-02-05 16:06:48

Abstract

This course is meant as an invitation to some key ideas and techniques in Geometric Analysis, with special emphasis on the theory of minimal surfaces. It is primarily conceived for advanced Bachelor or beginning Master students.

Objective

The goal of this course is to get a first introduction to minimal surfaces both in the Euclidean space and in Riemannian manifolds, and to see some analytic tools in action to solve natural geometric problems. Students are guided through different types of references (standard monographs, surveys, research articles), encouraged to compare them and to critically prepare some expository work on a chosen topic. This course takes the form of a working group, where interactions among students, and between students and instructor are especially encouraged.

Content

The minimal surface equation, examples and basic questions. Parametrized surfaces, first variation of the area functional, different characterizations of minimality. The Gauss map, basic properties. The Douglas-Rado approach, basic existence results for the Plateau problem. Monotonicity formulae and applications, including the Farey-Milnor theorem on knotted curves. The second variation formula, stability and Morse index. The Bernstein problem and its solution in the two-dimensional case. Total curvature, curvature estimates and compactness theorems. Classification results for minimal surfaces of low Morse index.

Resources

Literature

The three basic references that we will mostly refer to are the following ones: [Whi16] B. White, Introduction to minimal surface theory. Geometric analysis, 387-438, IAS/Park City Math. Ser., 22. American Mathematical Society, Providence, RI, 2016. [CM11] T. Colding, W. Minicozzi, A course in minimal surfaces. Graduate Studies in Mathematics, 121. American Mathematical Society, Providence, RI, 2011. xii+313 pp. [Oss86] R. Osserman, A survey of minimal surfaces. Second edition. Dover Publications, Inc., New York, 1986. vi+207 pp. Further, more specific references will be listed during the first introductory lectures.

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC

Examination

Type
ungraded semester performance

Registration & Places

Limited places (Special selection)
Signup Start
03.01.2022
Signup End
18.02.2022

Course Components

Type Title Time & Place Hours
seminar Seminar on Minimal Surfaces (an Invitation to Geometric Analysis)
  • Thu 16:15-18:00 (HG D 3.2)
26 h semesterly

Offered In

  • Mathematics Bachelor
    • Seminars (NOTICE: The number of seminar places is limited, and the special selection procedure should help to allocate the places not primarily according to the registration time. Everybody is waitlisted first when he/she tries to register for a seminar in myStudies. Moreover: Only one mathematics seminar can be chosen per semester.)
  • Mathematics Master
    • Seminars and Semester Papers
      • Seminars (NOTICE: The number of seminar places is limited, and the special selection procedure should help to allocate the places not primarily according to the registration time. Everybody is waitlisted first when he/she tries to register for a seminar in myStudies. Moreover: Only one mathematics seminar can be chosen per semester. In case you need to attend 2 seminars in this semester, please take contact with the Study Administration (email: ).)