# On blowup of regularized solutions to Jang equation and constant expansion surfaces

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Schoen-Yau proved the spacetime positive energy theorem by reducing

it to the time-symmetric (Riemannian) case using the Jang equation. To

acquire solutions to the Jang equation, they introduced a family of

regularized equations and took the limit of regularized solutions, whereas a

sequence of regularized solutions could blow up in some bounded regions

enclosed by apparent horizons. They analyzed the blowup behavior near but

outside of apparent horizons, but what happens inside remains unknown. In

this talk, we will discuss the blowup behavior inside apparent horizons

through two common geometric treatments: dilation and translation. We will

also talk about the relation between the limits of blowup regularized

solutions and constant expansion surfaces.