11 citations · 15 across the 11 of their papers we have counts for
11 papers
Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetime
Pengyu Le
The constant mass function foliation has been shown useful for studying the null Penrose inequality on a null hypersurface, because of the monotonicity formula of Hawking mass alon…
Lorentz polarisation and isoperimetric inequality in Minkowski spacetime
Pengyu Le
In this paper, we prove an isoperimetric inequality for the domain of dependence of a finite lightcone in the Minkowski spacetime of dimension greater than or equal to 3. The inequ…
On effective uniformization of 2-sphere and the stability
Pengyu Le
We provide a proof of effective uniformization for nearly round 2-spheres, utilizing an identity related to the third-order differential of the conformal factor. This identity is c…
A Lorentz invariant sharp Sobolev inequality on the circle
Pengyu Le
We prove the following sharp Sobolev inequality on the circle with…
Linearised perturbation of constant mass aspect function foliation in Schwarzschild black hole spacetime
Pengyu Le
We study the linearised perturbation of the constant mass aspect function foliation in a Schwarzschild black hole spacetime. In particular, we investigate the linearised perturbati…
Global regular null hypersurfaces in a perturbed Schwarzschild black hole exterior
Pengyu Le
The spherically symmetric null hypersurfaces in a Schwarzschild spacetime are smooth away from the singularities and foliate the spacetime. We prove the existence of more general f…
Note on strong cosmic censorship for spherically symmetric Einstein-dust model
Pengyu Le
In this note, we derive an ordinary differential equation for outgoing light rays in the spacetime of a spherically symmetric contracting dust cloud. The violation of strong cosmic…
Marginal tubes and foliations by marginal surfaces
Pengyu Le
In this paper, we introduce the notion of a marginal tube, which is a hypersurface foliated by marginal surfaces. It generalises the notion of a marginally trapped tube and several…
Marginally trapped surfaces in a perturbed Schwarzschild spacetime
Pengyu Le
The concept of a marginally trapped surface is important in the theory of general relativity. In the Schwarzschild black hole spacetime, its event horizon is foliated by marginally…
A proof of the Kazdan-Warner identity via the Minkowski spacetime
Pengyu Le
Any 2-dim Riemannian manifold with spherical topology can be embedded isometrically into a lightcone of the Minkowski spacetime. We apply this fact to give a proof of the Kazdan-Wa…
The intersection of a hyperplane with a lightcone in the Minkowski spacetime
Pengyu Le
Klainerman, Luk and Rodnianski derived an anisotropic criterion for formation of trapped surfaces in vacuum, extending the original trapped surface formation theorem of Christodoul…