Scalar Curvature via Local Extent

to related objects

Abstract: We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between (n + 1) points in infinitesimally small neighborhoods of a point. Since this characterization is purely in terms of the distance function, it could be used to approach the problem of defining the scalar curvature on a non-smooth metric space. In the second part we will discuss this issue, focusing in particular on Alexandrov spaces and surfaces with bounded integral curvature.

Location: Deutsche Nationalbibliothek Frankfurt am Main

Extent: Online-Ressource

Language: Englisch

Bibliographic citation: Scalar Curvature via Local Extent ; volume:6 ; number:1 ; year:2018 ; pages:146-164 ; extent:19
Analysis and geometry in metric spaces ; 6, Heft 1 (2018), 146-164 (gesamt 19)

Creator: Veronelli, Giona

DOI: 10.1515/agms-2018-0008

URN: urn:nbn:de:101:1-2024041116321032695537

Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.

Last update: 14.08.2025, 10:50 AM CEST

Data provider

This object is provided by:
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.

Show original at data provider

Associated

Veronelli, Giona

Other Objects (12)

Local and global scalar curvature rigidity of Einstein manifolds

Foliated Positive Scalar Curvature

Hochschulschrift

Scalar curvature and vector bundles

Positive scalar curvature and applications

Scalar curvature in discrete gravity

Volume and macroscopic scalar curvature

Boundary conditions for scalar curvature

zweidimensionales bewegtes Bild

Topological rigidity and positive scalar curvature

Hochschulschrift

The scalar curvature of homogeneous metrics

Prescribing scalar curvature in conformal geometry

Index Theory and Positive Scalar Curvature

Hochschulschrift

Index Theory and Positive Scalar Curvature

Local and global scalar curvature rigidity of Einstein manifolds

Foliated Positive Scalar Curvature

Hochschulschrift

Scalar curvature and vector bundles

Positive scalar curvature and applications

Scalar curvature in discrete gravity

Volume and macroscopic scalar curvature

Boundary conditions for scalar curvature

zweidimensionales bewegtes Bild

Topological rigidity and positive scalar curvature

Hochschulschrift

The scalar curvature of homogeneous metrics

Prescribing scalar curvature in conformal geometry

Index Theory and Positive Scalar Curvature

Hochschulschrift

Index Theory and Positive Scalar Curvature

Local and global scalar curvature rigidity of Einstein manifolds

Foliated Positive Scalar Curvature

Hochschulschrift

Scalar curvature and vector bundles

Positive scalar curvature and applications

Scalar curvature in discrete gravity

Volume and macroscopic scalar curvature

Boundary conditions for scalar curvature

zweidimensionales bewegtes Bild

Topological rigidity and positive scalar curvature

Hochschulschrift

The scalar curvature of homogeneous metrics

Prescribing scalar curvature in conformal geometry

Index Theory and Positive Scalar Curvature

Hochschulschrift

Index Theory and Positive Scalar Curvature

Cultural heritage institutions wishing to register will find more information here.

Fields marked * need to be filled in.

Username*

Please enter your username

Email*

Please enter your email address

Please do not fill this field

First name

Last name

Password*

Please enter your password

Confirm password*

Please enter the same password

I have read the terms of use and the privacy policy for the collection of personal data and accept them. *

This field is required.

I would like to subscribe to the newsletter of the Deutsche Digitale Bibliothek. See newsletter subscription info.

Account created

Your "My DDB" account has been successfully created. Before you can log in to your account, you must click the confirmation link in the message we just sent to the email address you provided.

Scalar Curvature via Local Extent

Object Details

References and Relationships

Contributors, Places and Time

Further information

Data provider

Associated

Other Objects (12)

Local and global scalar curvature rigidity of Einstein manifolds

Foliated Positive Scalar Curvature

Scalar curvature and vector bundles

Positive scalar curvature and applications

Scalar curvature in discrete gravity

Volume and macroscopic scalar curvature

Boundary conditions for scalar curvature

Topological rigidity and positive scalar curvature

The scalar curvature of homogeneous metrics

Prescribing scalar curvature in conformal geometry

Index Theory and Positive Scalar Curvature

Index Theory and Positive Scalar Curvature

Local and global scalar curvature rigidity of Einstein manifolds

Foliated Positive Scalar Curvature

Scalar curvature and vector bundles

Positive scalar curvature and applications

Scalar curvature in discrete gravity

Volume and macroscopic scalar curvature

Boundary conditions for scalar curvature

Topological rigidity and positive scalar curvature

The scalar curvature of homogeneous metrics

Prescribing scalar curvature in conformal geometry

Index Theory and Positive Scalar Curvature

Index Theory and Positive Scalar Curvature

Local and global scalar curvature rigidity of Einstein manifolds

Foliated Positive Scalar Curvature

Scalar curvature and vector bundles

Positive scalar curvature and applications

Scalar curvature in discrete gravity

Volume and macroscopic scalar curvature

Boundary conditions for scalar curvature

Topological rigidity and positive scalar curvature

The scalar curvature of homogeneous metrics

Prescribing scalar curvature in conformal geometry

Index Theory and Positive Scalar Curvature

Index Theory and Positive Scalar Curvature

Related objects

Reset password