9 citations · 22 across the 18 of their papers we have counts for
17 papers · 1 filter
Spectral Positive Mass Theorem for Asymptotically Hyperbolic 3-manifolds with Toroidal Infinity
Xiaoxiang Chai, Yimin Chen, Juncheol Pyo
We define a mass invariant adapted to the spectral scalar curvature for asymptotically hyperbolic 3-manifolds with toroidal infinity and show its positivity under a lower bound on…
Free boundary minimal annuli in
Pak Tung Ho, Juncheol Pyo, Keomkyo Seo
Let be a compact 3-dimensional Riemannian manifold with nonnegative Ricci curvature and a nonempty boundary . Fraser and Li \cite{Fraser&Li} established a compactne…
Spectral constant rigidity of warped product metrics
Xiaoxiang Chai, Juncheol Pyo, Xueyuan Wan
A theorem of Llarull says that if a smooth metric on the -sphere is bounded below by the standard round metric and the scalar curvature of is bounde…
Rigidity results for mean curvature flow graphical translators moving in non-graphical direction
John Man Shun Ma, Yuan Shyong Ooi, Juncheol Pyo
In this paper, we study the rigidity results of complete graphical translating hypersurfaces when the translating direction is not in the graphical direction. We proved that any en…
Some rigidity results on compact hypersurfaces with capillary boundary in Hyperbolic space
Yimin Chen, Juncheol Pyo
In this paper, we prove a Heintze-Karcher type inequality for capillary hypersurfaces supported on various hypersurfaces in the hyperbolic space. The equality case only occurs on c…
Weighted Hsiung-Minkowski formulas and rigidity of umbilical hypersurfaces
Kwok-Kun Kwong, Hojoo Lee, Juncheol Pyo
We use the weighted Hsiung-Minkowski integral formulas and Brendle's inequality to show new rigidity results. First, we prove Alexandrov type results for closed embedded hypersurfa…