401-3830-69L  Seminar on Minimal Surfaces

SemesterHerbstsemester 2019
DozierendeA. Carlotto
Periodizitäteinmalige Veranstaltung
KommentarThe total number of students who may take this course for credit is limited to twenty; however further students are welcome to attend.


401-3830-69 SSeminar on Minimal Surfaces28s Std.
Mo/2w16:15-18:00HG G 26.3 »
Di/2w15:15-17:00HG G 26.1 »
16.12.16:15-18:00HG G 19.2 »
17.12.15:15-17:00HG G 26.1 »
A. Carlotto


KurzbeschreibungThis 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.
LernzielThe 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 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.
InhaltThe 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.
LiteraturThree basic references that we will mostly refer to are the following ones:

1) B. White, Lectures on minimal surface theory, Geometric analysis, 387–438, IAS/Park City Math. Ser., 22, Amer. Math. Soc., Providence, RI, 2016.

2) T. Colding, W. Minicozzi, A course in minimal surfaces. Graduate Studies in Mathematics, 121. American Mathematical Society, Providence, RI, 2011. xii+313 pp.

3) 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 two introductory lectures.
Voraussetzungen / BesonderesThe content of the first two years of the Bachelor program in Mathematics, in particular all courses in Real and Complex Analysis, Measure Theory, Topology.

Some familiarity with the language of Differential Geometry, although not a formal pre-requisite, might be highly helpful. Finally, a first course on elliptic equations (especially on basic topics like Schauder estimates and the maximum principle) might also be a plus.


Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs
ECTS Kreditpunkte4 KP
PrüfendeA. Carlotto
Formunbenotete Semesterleistung
RepetitionRepetition nur nach erneuter Belegung der Lerneinheit möglich.


Es werden nur die öffentlichen Lernmaterialien aufgeführt.


Keine Informationen zu Gruppen vorhanden.


PlätzeMaximal 20
VorrangDie Belegung der Lerneinheit ist nur durch die primäre Zielgruppe möglich
Primäre ZielgruppeMathematik BSc (404000) ab Semester 05
Mathematik MSc (437000)
Angewandte Mathematik MSc (437100)
Mathematik (Mobilität) (448000)
WartelisteBis 30.09.2019

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