On a Family of Quasimetric Spaces in Generalized Potential Theory-Reference-Cited by-同舟云学术

On a Family of Quasimetric Spaces in Generalized Potential Theory

Published:2022-01-29 Issue:4 Volume:32 Page:
ISSN:1050-6926
Container-title:The Journal of Geometric Analysis
language:en
Short-container-title:J Geom Anal

Author:

Åhag Per,Czyż Rafał

Abstract

AbstractWe construct a family of quasimetric spaces in generalized potential theory containing m-subharmonic functions with finite (p, m)-energy. These quasimetric spaces will be viewed both in

$${\mathbb {C}}^n$$

C n and in compact Kähler manifolds, and their convergence will be used to improve known stability results for the complex Hessian equations.

Funder

Umea University

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology

Link

https://link.springer.com/content/pdf/10.1007/s12220-021-00857-0.pdf

Reference40 articles.

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2. Abdullaev, B.I., Sadullaev, A.: Capacities and Hessians in the class of $$m$$-subharmonic functions. Dokl. Math. 87(1), 88–90 (2013)

3. Åhag, P., Czyż, R., Phạm, H.H.: Concerning the energy class $$\cal{E}$$ for $$0

4. Åhag, P., Czyż, R.: Modulability and duality of certain cones in pluripotential theory. J. Math. Anal. Appl. 361(2), 302–321 (2010)

5. Åhag, P., Czyż, R., Hed, L.: The geometry of $$m$$-hyperconvex domains. J. Geom. Anal. 28(4), 3196–3222 (2018)

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