Rigidity and Non-rigidity Results on the Sphere

  title={Rigidity and Non-rigidity Results on the Sphere},
  author={Fengbo Hang and Xiaodong Wang},
It is a simple consequence of the maximum principle that a superharmonic function u on Rn(i. e. ∆u ≤ 0) which is 1 near infinity is identically 1 on Rn (throughout this paper, n ≥ 3). Geometrically this means that one can not conformally deform the Euclidean metric in a bounded region without decreasing the scalar curvature somewhere. In fact there is a much stronger result: one can not have any compact deformation of the Euclidean metric without decreasing the scalar curvature somewhere, i. e… CONTINUE READING

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 12 references

Scalar curvature deformation and a gluing construction for the Einstein constraint equations

  • J. Corvino
  • Comm. Math. Phys. 214
  • 2000
Highly Influential
3 Excerpts

Scalar curvature and hammocks

  • J. Lohkamp
  • Math. Ann. 313
  • 1999
1 Excerpt

Scalar curvature rigidity of the hemisphere

  • M. Min-Oo
  • 1995
1 Excerpt

Lectures on Differential Geometry

  • R. Schoen, S.-T. Yau
  • 1994

Einstein Manifolds

  • A. Besse
  • Springer-Verlag, New York
  • 1987

Some Regularity Theorems in Riemannian Geometry

  • D. DeTurck, J. Kazdan
  • Ann. Sci. cole Norm. Sup. (4) 14
  • 1981
1 Excerpt

Similar Papers

Loading similar papers…