# Conformally bending three-manifolds with boundary

Matthew Gursky^{[1]}; Jeffrey Streets^{[2]}; Micah Warren^{[2]}

- [1] University of Notre Dame Department of Mathematics Notre Dame, IN 46556 (USA)
- [2] Princeton University Fine Hall Princeton, NJ 08544 (USA)

Annales de l’institut Fourier (2010)

- Volume: 60, Issue: 7, page 2421-2447
- ISSN: 0373-0956

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topGursky, Matthew, Streets, Jeffrey, and Warren, Micah. "Conformally bending three-manifolds with boundary." Annales de l’institut Fourier 60.7 (2010): 2421-2447. <http://eudml.org/doc/116340>.

@article{Gursky2010,

abstract = {Given a three-dimensional manifold with boundary, the Cartan-Hadamard theorem implies that there are obstructions to filling the interior of the manifold with a complete metric of negative curvature. In this paper, we show that any three-dimensional manifold with boundary can be filled conformally with a complete metric satisfying a pinching condition: given any small constant, the ratio of the largest sectional curvature to (the absolute value of) the scalar curvature is less than this constant. This condition roughly means that the curvature is “almost negative”, in a scale-invariant sense.},

affiliation = {University of Notre Dame Department of Mathematics Notre Dame, IN 46556 (USA); Princeton University Fine Hall Princeton, NJ 08544 (USA); Princeton University Fine Hall Princeton, NJ 08544 (USA)},

author = {Gursky, Matthew, Streets, Jeffrey, Warren, Micah},

journal = {Annales de l’institut Fourier},

keywords = {Almost negative curvature; conformal filling; fully nonlinear equations; manifold with boundary; conformal bending; scalar curvature; pinching of sectional curvature; almost negative curvature},

language = {eng},

number = {7},

pages = {2421-2447},

publisher = {Association des Annales de l’institut Fourier},

title = {Conformally bending three-manifolds with boundary},

url = {http://eudml.org/doc/116340},

volume = {60},

year = {2010},

}

TY - JOUR

AU - Gursky, Matthew

AU - Streets, Jeffrey

AU - Warren, Micah

TI - Conformally bending three-manifolds with boundary

JO - Annales de l’institut Fourier

PY - 2010

PB - Association des Annales de l’institut Fourier

VL - 60

IS - 7

SP - 2421

EP - 2447

AB - Given a three-dimensional manifold with boundary, the Cartan-Hadamard theorem implies that there are obstructions to filling the interior of the manifold with a complete metric of negative curvature. In this paper, we show that any three-dimensional manifold with boundary can be filled conformally with a complete metric satisfying a pinching condition: given any small constant, the ratio of the largest sectional curvature to (the absolute value of) the scalar curvature is less than this constant. This condition roughly means that the curvature is “almost negative”, in a scale-invariant sense.

LA - eng

KW - Almost negative curvature; conformal filling; fully nonlinear equations; manifold with boundary; conformal bending; scalar curvature; pinching of sectional curvature; almost negative curvature

UR - http://eudml.org/doc/116340

ER -

## References

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