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

Clara L. Aldana; Gilles Carron; Samuel Tapie

doi:10.2140/apde.2021.14.2163

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

Analysis & PDE ◽

10.2140/apde.2021.14.2163 ◽

2021 ◽

Vol 14 (7) ◽

pp. 2163-2205

Author(s):

Clara L. Aldana ◽

Gilles Carron ◽

Samuel Tapie

Keyword(s):

Conformal Metrics ◽

Curvature Bounds

Download Full-text

Boundary expansions of complete conformal metrics with negative Ricci curvatures

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-021-02010-9 ◽

2021 ◽

Vol 60 (4) ◽

Author(s):

Yue Wang

Keyword(s):

Conformal Metrics

Download Full-text

Remarks on Manifolds with Two-Sided Curvature Bounds

Analysis and Geometry in Metric Spaces ◽

10.1515/agms-2020-0122 ◽

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.

Download Full-text

Topological tools for the prescribed scalar curvature problem on S n

Open Mathematics ◽

10.2478/s11533-014-0443-9 ◽

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].

Download Full-text