Vol. 15, No. 3, 2022

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 6, 1375–1616
Issue 5, 1131–1373
Issue 4, 891–1130
Issue 3, 567–890
Issue 2, 273–566
Issue 1, 1–272

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
Regular domains and surfaces of constant Gaussian curvature in 3-dimensional affine space

Xin Nie and Andrea Seppi

Vol. 15 (2022), No. 3, 643–697
Abstract

Generalizing the notion of domains of dependence in the Minkowski space, we define and study regular domains in the affine space with respect to a proper convex cone. In three dimensions, we show that every proper regular domain is uniquely foliated by some particular surfaces with constant affine Gaussian curvature. The result is based on the analysis of a Monge–Ampère equation with extended real-valued lower semicontinuous boundary condition.

Keywords
domain of dependence, affine differential geometry, affine Gauss–Kronecker curvature, Monge–Ampère equation
Mathematical Subject Classification 2010
Primary: 53A15
Secondary: 35J96, 53C42
Milestones
Received: 1 September 2019
Revised: 2 July 2020
Accepted: 13 November 2020
Published: 10 June 2022
Authors
Xin Nie
Shing-Tung Yau Center of Southeast University
Southeast University
Nanjing
China
Andrea Seppi
CNRS and Université Grenoble Alpes
Gières
France