DIFFERENTIAL GEOMETRY SEMINAR

(Alex Freire, Bo Guan, Conrad Plaut)

Tuesdays, 3:35- 4:30, Ayres 309B

ANNOUNCEMENTS, FALL 1999

1. September 7, 1999

Title: The Riemannian Penrose Conjecture

Speaker: Alex Freire

Abstract: The conjecture provides a lower estimate for

the ADM mass of an asymptotically flat 3-manifold with positive

scalar curvature and minimal boundary in terms of the area of the boundary

(generalizing the positive mass theorem of Schoen and Yau). I

will present the main ingredients in the recent proof by Huisken

and Ilmanen: the inverse mean curvature flow, monotonicity of

the Hawking mass and an asymptotic inequality relating the

Hawking and ADM masses.

2. September 14, 1999

Title: The Riemannian Penrose Conjecture, Part II

Speaker: Alex Freire

Abstract: I'll review the definitions of ADM mass and

Hawking mass and the statement of the main theorem in the

paper by Huisken and Ilmanen, then prove monotonicty of

the Hawking mass in the smooth case and discuss the existence of

weak solutions of the inverse mean curvature flow.

3. September 21,1999

Title: The Riemannian Penrose Conjecture, Part III

Speaker: Alex Freire

Abstract: Different notions of weak solution for the inverse

mean curvature flow will be discussed.

4. September 28, 1999

Title: The Riemannian Penrose Conjecture (Conclusion)

Speaker: Alex Freire

Abstract: Discussion of existence of weak solutions and the

symptotics of the Hawking mass in AF 3-manifolds

5. October 5, 1999

Title: Polynomial growth harmonic functions on Riemannian

manifolds (after T.Colding and W.Minicozzi II)

Speaker: Bo Guan

6. October 19,1999

Title: Polynomial growth harmonic functions on manifolds II

Speaker: Bo Guan

7. October 26, 1999

Title: .Polynomial growth harmonic functions on manifolds III

Speaker: Bo Guan