Existence of Metrics with Prescribed Scalar Curvature on the Volume Element Preserving Deformation

2006/12/22 by Zhi-Zhang Wang, Wang, Zhi-Zhang
Mathematics · #35L70 #53C21 #58J45 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG #msc:35L70 #msc:53C21 #msc:58J45

paper · pdf · doi:10.48550/arxiv.math/0612686

32 pages

arxiv created 2006/12/22 · arxiv updated 2009/12/01

Abstract

In this paper,we obtain two results on closed Reimainnian manifold M× [0,T].When T is small enough,to any prescribed scalar curvature, the existence and uniqueness of metrics are obtained on the volume element preserving deformation.When T is large and the given scalar curvature is small enough,the same result holds.

Related

• Deformation of Scalar Curvature and Volume
• Scalar curvature deformations with non-compact boundaries
• The prescribed scalar curvature problem for metrics with unit total volume
• Extremal metrics involving scalar curvature
• Some obstructions to positive scalar curvature on a noncompact manifold