Mass, the Einstein Constraint Equations, and the Penrose Inequality Conjecture: September 18-22, 2023

Organizing Committee:
• Carla Cederbaum (University of Tübingen)
• Greg Galloway (University of Miami)
• Lan-Hsuan Huang (University of Connecticut Storrs)
• Jim Isenberg (University of Oregon)
• Marcus Khuri (Stony Brook University)
• David Maxwell (University of Alaska Fairbanks)

Scientific Committee:
• Anna Sakovich (Uppsala University)
• Richard Schoen (UC Irvine)
• Mu-Tao Wang (Columbia University)

The ADM mass and other such quantities, generally involve initial data sets for Einstein’s gravitational field equations. These equations impose
constraints on initial data sets. The constraints take the form of an underdetermined set of partial differential equations. One particularly effective way to replace these constraints with an elliptic determined system is via the conformal method. This method has been highly successful in parametrizing and constructing solutions of the constraints, with constant mean curvature. The recent work of Maxwell and Isenberg shows that the conformal method also works very well for a wide variety of matter fields coupled to Einstein’s equations. While the conformal method can be extended to initial data sets which are close to constant mean curvature, it is ineffective for initial data sets which are far from constant mean curvature. One possible approach for working with far from constant mean curvature initial data sets is the drift method, developed by Maxwell. This, as well as other possible approaches for constructing far from constant mean curvature solutions of the Einstein constraints, will
be explored at this workshop.