Name Gerhard Huisken | ||

## Lecture 1 mean curvature flow gerhard huisken

**Gerhard Huisken** (born May 20, 1958) is a German mathematician.

## Contents

- Lecture 1 mean curvature flow gerhard huisken
- Lecture 4 mean curvature flow gerhard huisken
- Life
- Work
- Honours and awards
- Publications
- References

## Lecture 4 mean curvature flow gerhard huisken

## Life

After finishing high school in 1977, Huisken took up studies in mathematics at Heidelberg University. In 1982, one year after his diploma graduation, he completed his PhD at the University of Heidelberg. The topic of his dissertation were non-linear partial differential equations (*Reguläre Kapillarflächen in negativen Gravitationsfeldern*).

From 1983 to 1984, Huisken was a researcher at the Centre for Mathematical Analysis at the Australian National University (ANU) in Canberra. There, he turned to differential geometry, in particular problems of mean curvature flows and applications in general relativity. In 1985, he returned to the University of Heidelberg, earning his habilitation in 1986. After some time as a visiting professor at the University of California, San Diego, he returned to ANU from 1986 to 1992, first as a Lecturer, then as a Reader. In 1991, he was a visiting professor at Stanford University. From 1992 to 2002, Huisken was a full professor at the University of Tübingen, serving as dean of the faculty of mathematics from 1996 to 1998. From 1999 to 2000, he was a visiting professor at Princeton University.

In 2002, Huisken became a director at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) in Potsdam and, at the same time, an honorary professor at the Free University of Berlin. In April 2013, he took up the post of director at the Mathematical Research Institute of Oberwolfach, together with a professorship at Tübingen University. He remains an external scientific member of the Max Planck Institute for Gravitational Physics.

Among Huisken's PhD students was Simon Brendle.

## Work

Huisken's work is on the intersection of analysis, geometry, and physics. Numerous phenomena in mathematical physics and geometry are related to curves, surfaces and spaces. In particular, Huisken has worked on the deformation of surfaces over time, in situations where the rules of deformation are determined by the geometry of those surfaces themselves. For instance, Huisken's monotonicity formula is an important tool in the analysis of the mean curvature flow.

Gerhard Huisken has made major contributions to general relativity. In 1997, together with Tom Ilmanen (ETH Zurich), he was able to prove the Penrose conjecture for black holes for the case of a three-dimensional Riemannian manifold with positive scalar curvature, in the presence of a single black hole.

1998 he was an invited speaker at the International Congress of Mathematicians in Berlin ("Evolution of hypersurfaces by their curvature in Riemannian Manifolds").

## Honours and awards

Huisken is a fellow of the Heidelberg Academy for Sciences and Humanities, the Berlin-Brandenburg Academy of Sciences and Humanities, the Academy of Sciences Leopoldina, and the American Mathematical Society.

## Publications

*Flow by mean curvature of convex surfaces into spheres*,

*J. Differential Geom.*20 (1984), no. 1, 237–266.

*Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature*,

*Invent. Math.*84 (1986), no. 3, 463–480.

*Mean curvature evolution of entire graphs*,

*Ann. of Math.*(2) 130 (1989), no. 3, 453–471.

*Asymptotic behavior for singularities of the mean curvature flow*,

*J. Differential Geom.*31 (1990), no. 1, 285–299.

*Interior estimates for hypersurfaces moving by mean curvature*,

*Invent. Math.*105 (1991), no. 3, 547–569.

*Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature*,

*Invent. Math.*124 (1996), no. 1–3, 281–311.

*Convexity estimates for mean curvature flow and singularities of mean convex surfaces*,

*Acta Math.*183 (1999), no. 1, 45–70

*The inverse mean curvature flow and the Riemannian Penrose inequality*,

*J. Differential Geom.*59 (2001), no. 3, 353–437.

*Mean curvature flow with surgeries of two-convex hypersurfaces*,

*Invent. Math.*175 (2009), no. 1, 137–221.

*Evolution Equations in Geometry*, in Engquist, Schmid (Ed.)

*Mathematics Unlimited – 2001 and beyond*, Springer 2001