scholarly journals Some Conformal Invariants from the Noncommutative Residue for Manifolds with Boundary

2007 ◽  
Author(s):  
William J. Ugalde
Keyword(s):  
Manifolds With Boundary ◽  
Conformal Invariants ◽  
Noncommutative Residue

scholarly journals The Noncommutative Residue for Manifolds with Boundary

1996 ◽  
Vol 142 (1) ◽  
pp. 1-31 ◽  
Author(s):  
Boris V. Fedosov ◽  
François Golse ◽  
Eric Leichtnam ◽  
Elmar Schrohe
Keyword(s):  
Manifolds With Boundary ◽  
Noncommutative Residue

scholarly journals Conformal invariants from nodal sets. II. Manifolds with boundary

2021 ◽  
Author(s):  
Graham Cox ◽  
Dmitry Jakobson ◽  
Mikhail Karpukhin ◽  
Yannick Sire
Keyword(s):  
Manifolds With Boundary ◽  
Conformal Invariants ◽  
Nodal Sets

scholarly journals An Obata-type theorem on compact Einstein manifolds with boundary

2021 ◽  
Author(s):  
Kazuo Akutagawa
Keyword(s):  
Boundary Condition ◽  
Smooth Boundary ◽  
Type Theorem ◽  
Type Inequality ◽  
Einstein Metric ◽  
Manifolds With Boundary ◽  
Einstein Manifolds ◽  
Conformal Class ◽  
Totally Geodesic ◽  
Yamabe Constant

AbstractWe show a kind of Obata-type theorem on a compact Einstein n-manifold $$(W, \bar{g})$$ ( W , g ¯ ) with smooth boundary $$\partial W$$ ∂ W . Assume that the boundary $$\partial W$$ ∂ W is minimal in $$(W, \bar{g})$$ ( W , g ¯ ) . If $$(\partial W, \bar{g}|_{\partial W})$$ ( ∂ W , g ¯ | ∂ W ) is not conformally diffeomorphic to $$(S^{n-1}, g_S)$$ ( S n - 1 , g S ) , then for any Einstein metric $$\check{g} \in [\bar{g}]$$ g ˇ ∈ [ g ¯ ] with the minimal boundary condition, we have that, up to rescaling, $$\check{g} = \bar{g}$$ g ˇ = g ¯ . Here, $$g_S$$ g S and $$[\bar{g}]$$ [ g ¯ ] denote respectively the standard round metric on the $$(n-1)$$ ( n - 1 ) -sphere $$S^{n-1}$$ S n - 1 and the conformal class of $$\bar{g}$$ g ¯ . Moreover, if we assume that $$\partial W \subset (W, \bar{g})$$ ∂ W ⊂ ( W , g ¯ ) is totally geodesic, we also show a Gursky-Han type inequality for the relative Yamabe constant of $$(W, \partial W, [\bar{g}])$$ ( W , ∂ W , [ g ¯ ] ) .

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