Survey on the Asymptotic Dirichlet Problem for the Minimal Surface Equation

Heinonen, Esko

doi:10.1007/978-3-030-68541-6_7

Springer Proceedings in Mathematics &Amp; Statistics

2021

DOI: 10.1007/978-3-030-68541-6_7

|View full text |Cite

Survey on the Asymptotic Dirichlet Problem for the Minimal Surface Equation

Esko Heinonen

Help me understand this report

View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Bernstein and Half-Space Properties for Minimal Graphs Under Ricci Lower Bounds

Colombo¹,

Magliaro²,

Mari³

et al. 2022

International Mathematics Research Notices

View full text Add to dashboard Cite

In this paper, we prove a new gradient estimate for minimal graphs defined on domains of a complete manifold $M$ with Ricci curvature bounded from below. This enables us to show that positive, entire minimal graphs on manifolds with non-negative Ricci curvature are constant and that complete, parabolic manifolds with Ricci curvature bounded from below have the half-space property. We avoid the need of sectional curvature bounds on $M$ by exploiting a form of the Ahlfors–Khas’minskii duality in nonlinear potential theory.

show abstract

Bernstein and Half-Space Properties for Minimal Graphs Under Ricci Lower Bounds

Colombo¹,

Magliaro²,

Mari³

et al. 2022

International Mathematics Research Notices

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Survey on the Asymptotic Dirichlet Problem for the Minimal Surface Equation

Cited by 1 publication

References 45 publications

Bernstein and Half-Space Properties for Minimal Graphs Under Ricci Lower Bounds

Bernstein and Half-Space Properties for Minimal Graphs Under Ricci Lower Bounds

Contact Info

Product

Resources

About