scholarly journals A∞-weights and compactness of conformal metrics under Ln∕2 curvature bounds

2021 ◽  
Vol 14 (7) ◽  
pp. 2163-2205
Author(s):  
Clara L. Aldana ◽  
Gilles Carron ◽  
Samuel Tapie
Keyword(s):  
Conformal Metrics ◽  
Curvature Bounds

scholarly journals Remarks on Manifolds with Two-Sided Curvature Bounds

2021 ◽  
Vol 9 (1) ◽  
pp. 53-64
Author(s):  
Vitali Kapovitch ◽  
Alexander Lytchak
Keyword(s):  
Distance Functions ◽  
Cut Locus ◽  
Bounded Curvature ◽  
Curvature Bounds ◽  
Positive Reach

Abstract We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.

Topological tools for the prescribed scalar curvature problem on S n

2014 ◽  
Vol 12 (12) ◽  
Author(s):  
Dina Abuzaid ◽  
Randa Ben Mahmoud ◽  
Hichem Chtioui ◽  
Afef Rigane
Keyword(s):  
Scalar Curvature ◽  
Conformal Metrics ◽  
Standard Sphere ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Hopf Formula ◽  
Curvature Problem ◽  
Formula Type

AbstractIn this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

scholarly journals Smoothing Riemannian metrics with Ricci curvature bounds

1996 ◽  
Vol 90 (1) ◽  
pp. 49-61 ◽  
Author(s):  
Xianzhe Dai ◽  
Guofang Wei ◽  
Rugang Ye
Keyword(s):  
Ricci Curvature ◽  
Riemannian Metrics ◽  
Curvature Bounds

Blowing up with infinite energy of conformal metrics on Sn

1999 ◽  
Vol 24 (5-6) ◽  
pp. 785-799 ◽  
Author(s):  
Chiun-Chuan Chen ◽  
Chiun-Chuan Chen ◽  
Chang-Shou Lin ◽  
Chang-Shou Lin
Keyword(s):  
Conformal Metrics ◽  
Blowing Up ◽  
Infinite Energy
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