We prove existence of instantaneously complete Yamabe flows on hyperbolic space of arbitrary dimension m≥ 3. The initial metric is assumed to be conformally hyperbolic with conformal factor and scalar curvature bounded from above. We do not require initial completeness or bounds on the Ricci curvature. If the initial data are rotationally symmetric, the solution is proven to be unique in the class of instantaneously complete, rotationally symmetric Yamabe flows.
Instantaneously complete Yamabe flow on hyperbolic space / Schulz, Mario B.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 58:6(2019). [10.1007/s00526-019-1634-9]
Instantaneously complete Yamabe flow on hyperbolic space
Schulz, Mario B.
2019-01-01
Abstract
We prove existence of instantaneously complete Yamabe flows on hyperbolic space of arbitrary dimension m≥ 3. The initial metric is assumed to be conformally hyperbolic with conformal factor and scalar curvature bounded from above. We do not require initial completeness or bounds on the Ricci curvature. If the initial data are rotationally symmetric, the solution is proven to be unique in the class of instantaneously complete, rotationally symmetric Yamabe flows.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
