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* July 13, 1936

Stefan Hildebrandt

Mathematical Institute

Academic career

1954-1960	Studies of mathematics and physics,
	Leipzig and Mainz University
1960	Dipl. Math., Mainz University
1961	Dr. rer. nat., Mainz University
1961-1963	Assistant, Mainz University
1963-1965	Research scientist, Courant Institute,
	New York University
1965	Habilitation, Mainz University
1967	H4 professor, Mainz University
1970	H4/C4 professor, Bonn University
2001	Professor emeritus, Bonn University

Awards and honours

1985, Member Deutsche Akademie der Naturforscher Leopoldina (Halle)
1994, Karl Georg Christian von Staudt-Preis, Erlangen
1995, Dr. rer. nat. h. c. Bochum University
1997, Member Nordrhein-Westfälische Akademie der Wissenschaften (Düsseldorf)
2001, Dr. rer. nat. h. c. Leipzig University and Düsseldorf University

Editorship

Manuscipta Mathematica (1970-1986); Analyse Non Linéaire (since 1982); Calculus of Variations (1993-2005); Oxford University Press (since 1995)

Research projects and activities

Calculus of variations, conformal mappings and uniformization, minimal surfaces

Research profile

Nonlinear partial differential equations, calculus of variations, geometric differential equations, conformal mappings

Contribution to research area "Geometry of differential operators"

We have started to understand the properties of solutions to the Plateau problem for Cartan functionals [16], [15], [14], [13], a higher dimensional analog of Finsler geometry. Important questions concerning regularity and the development of singularities are unsolved.

Contribution to research area "Shape, pattern and partial differential equations"

It is interesting to understand how geometric data determine the shape of solutions to geometric differential equations. This we have worked out for minimal surfaces with singular boundary conditions [9], [10], [11], [12], [8], [6]. Of particular interest is the conformal structure of manifolds and generalized surfaces. We have found a new variational approach to this kind of problems [18], [17].

Selected PhD Students

Klaus Steffen, now: Full Professor Düsseldorf University
Helmuth Kaul, now: professor Tübingen University
Claus Gerhardt, now: professor, Heidelberg University
Josef Bemelmans, now: full professor TH Aachen
Jürgen Jost, now: professor Leipzig University, Director of the MPIM Leipzig
Ulrich Dierkes, now: full professor Duisburg University
Rugang Ye, now: full professor University of California at Santa Barbara
Ernst Kuwert, now: full professor Freiburg University
Leung-Fu Cheung now: professor TU Hongkong
Heiko von der Mosel, now: professor TH Aachen
Ruben Jakob, now: DFG-Researcher

Habilitations

Klaus Steffen, now: full professor Düsseldorf University
Helmuth Kaul, now: professor Tübingen University
Michael Reeken, now: full professor Wuppertal University
Claus Gerhardt, now: professor, Heidelberg University
Josef Bemelmans, now: full professor TH Aachen,
Jürgen Jost, now: professor Leipzig University, Director of the MPIM Leipzig
Ernst Kuwert, now: full professor Freiburg University
Heiko von der Mosel, now: professor TH Aachen
Stefan Müller, now: professor Leipzig University, Director of the MPIM Leipzig

Publications

[1]	DIERKES, U., HILDEBRANDT, S., AND LEWY, H. On the analyticity of minimal surfaces at movable boundaries of prescribed length. J. Reine Angew. Math. 379 (1987), 100-114.
[2]	GRÜTER, M., HILDEBRANDT, S., AND NITSCHE, J. C. C. Regularity for stationary surfaces of constant mean curvature with free boundaries. Acta Math. 156 (1986), 119-152.
[3]	HILDEBRANDT, S. Harmonic mappings of Riemannian manifolds. C.I.M.E. Lectures at Montecatini 1984. Springer Lecture Notes in Math. 1161 (1985), 1-117.
[4]	HILDEBRANDT, S. Contact transforms, Huygens's principle, and calculus of variations. Calc. Var. 2 (1994), 249-281.
[5]	HILDEBRANDT, S. On Hölder's transformation. J. Math. Sci. Univ. Tokyo 1 (1994), 1-21.
[6]	HILDEBRANDT, S., DIERKES, U., KÜSTER, A., AND WOHLRAB, D. Minimal surfaces. Grundlehren der math. Wiss., vol. 295/296. Springer, Berlin, 1992.
[7]	HILDEBRANDT, S., AND GIAQUINTA, M. Calculus of variations. Grundlehren der math. Wiss., vol. 310/311. Springer, Berlin/Heidelberg, 1995/1996.
[8]	HILDEBRANDT, S., AND SAUVIGNY, F. Uniqueness of stable minimal surfaces with partially free boundaries. J. Math. Soc. Japan 47 (1995), 423-440.
[9]	HILDEBRANDT, S., AND SAUVIGNY, F. Minimal surfaces in a wedge. I. Calc. Var. 5 (1997), 99-115.
[10]	HILDEBRANDT, S., AND SAUVIGNY, F. Minimal surfaces in a wedge. II. Archiv der Math. 69 (1997), 164-176.
[11]	HILDEBRANDT, S., AND SAUVIGNY, F. Minimal surfaces in a wedge. III. J. Reine Angew. Math. 514 (1999), 71-101.
[12]	HILDEBRANDT, S., AND SAUVIGNY, F. Minimal surfaces in a wedge. IV. Calc. Var. 8 (1999), 71-90.
[13]	HILDEBRANDT, S., AND VON DER MOSEL, H. On two-dimensional parametric variational problems. Calc. Var. 9 (1999), 249-267.
[14]	HILDEBRANDT, S., AND VON DER MOSEL, H. Dominance functions for parametric Lagrangians. Geometric analysis and nonlinear partial differential equations. (2003), 297-326.
[15]	HILDEBRANDT, S., AND VON DER MOSEL, H. Plateau's problem for parametric double integrals. I. Existence and regularity in the interior. Comm. Pure Appl. Math. 56 (2003), 926-955.
[16]	HILDEBRANDT, S., AND VON DER MOSEL, H. Plateau's problem for parametric double integrals. II. Regularity at the boundary. J. Reine Angw. Math. 565 (2003), 207-233.
[17]	HILDEBRANDT, S., AND VON DER MOSEL, H. Conformal representation of surfaces, and Plateau's problem for Cartan functionals. Riv. Mat. Univ. Parma 7 (2005), 1-43.
[18]	HILDEBRANDT, S., AND VON DER MOSEL, H. On Lichtenstein's theorem about globally conformal mappings. Calc. Var. 23 (2005), 415-424.

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