Differential Geometry II – Geometry of Submanifolds
Lecture: Mo, Mi, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
Teacher: Guofang Wang
Assistant: Xuwen Zhang
Language: in German
In the lecture, we discuss the geometry of the sub-manifolds of Euclidian spaces. Examples of such sub-manifolds are curves in the plane and surfaces in the 3-dimensional space. In the 1st part we introduce the external geometry of the sub-manifold, e.g. the second fundamental form, the mean curvature, the first variation of the area, the equations of Gauss, Codazzi and Ricci. In the 2nd part we examine tminimal hypersurfaces (minimal surfaces), the hypersurface with constant mean curvature and the geometric inequalities, the isoperimetric inequality and its generalisations.
Analysis III and "Differential Geometry" or "Curves and Surfaces"
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Undergraduate seminar: One-Dimensional Maximum Principle
Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting 05.02., 16:00, SR 125, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Guofang Wang
Assistant: Xuwen Zhang
Language: in German
Analysis I and II
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Guofang Wang
Assistant: Christine Schmidt, Xuwen Zhang
Language: in German
A large number of different problems from the natural sciences and geometry lead to partial differential equations. Consequently, there can be no talk of an all-encompassing theory. Nevertheless, there is a clear picture for linear equations, which is based on three prototypes: the potential equation \(-\Delta u = f\), the heat equation \(u_t - \Delta u = f\) and the wave equation \(u_{tt} - \Delta u = f\), which we will examine in the lecture.
Required: Analysis III \ Recommended: Complex Analysis ({\em Funktionentheorie})
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Mo, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
Teacher: Xuwen Zhang
Language: in English
We will study functions of bounded variation, which are functions whose weak first partial derivatives are Radon measures. This is essentially the weakest definition of a function to be differentiable in the measure-theoretic sense. After discussing the basic properties of them, we move on to the study of sets of finite perimeter, which are Lebesgue measurable sets in the Euclidean space whose indicator functions are BV functions. Sets of finite perimeter are fundamental in the modern Calculus of Variations as they generalize in a natural measure-theoretic way the notion of sets with regular boundaries and possess nice compactness, thus appearing in many Geometric Variational problems. If time permits, we will discuss the (capillary) sessile drop problem as one important application.
Required: Basic knowledge in measure theory and analysis is required.
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting 17.07., 16:00
Preparation meetings for talks: Dates by arrangement
Teacher: Guofang Wang
Assistant: Xuwen Zhang
Language: Talk/participation possible in German and English
Minimal surfaces are surfaces in space with a “minimal” area and can be described using holomorphic functions. They occur, for example in the investigation of soap skins and the construction of stable objects (e.g. in architecture). In the investigation of minimal surfaces elegant methods from various mathematical fields such as function theory, calculus of variations, differential geometry and partial differential equations. are applied.
Required: Analysis III or knowledge about multidimensional integration and complex analysis. \ Recommended: Elementary knowledge about differential geometry.
Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)