30 citations · 143 across the 34 of their papers we have counts for
6 papers · 1 filter
On the Morse Index with Constraints I: An Abstract Formulation
Hung Tran, Detang Zhou
In this sequence, we first prove an abstract Morse index theorem in a Hilbert space modeling a variational problem with constraints. Then, our abstract formulation is applied to st…
On the Morse Index with Constraints II: Applications
Hung Tran, Detang Zhou
This is the second paper in our sequence. Here, we apply our abstract Morse index formulation developed in the previous paper to study several optimization set-ups with constraints…
Hopf type theorems for self-similar solutions of curvature flows in
Hilário Alencar, Gregório Silva Neto, Detang Zhou
In this paper we prove rigidity results for two-dimensional, closed, immersed, non-necessarily convex, self-similar solutions of a wide class of fully non-linear parabolic flows in…
Four-dimensional complete gradient shrinking Ricci solitons
Huai-Dong Cao, Ernani Ribeiro, Detang Zhou
In this article, we study four-dimensional complete gradient shrinking Ricci solitons. We prove that a four-dimensional complete gradient shrinking Ricci soliton satisfying a point…
Volume growth estimates for Ricci solitons and quasi-Einstein manifolds
Xu Cheng, Ernani Ribeiro, Detang Zhou
In this article, we provide some volume growth estimates for complete noncompact gradient Ricci solitons and quasi-Einstein manifolds similar to the classical results by Bishop, Ca…
Hopf type Theorem for Self-Shrinkers
Hilário Alencar, Gregório Silva Neto, Detang Zhou
In this paper, we prove that a two-dimensional self-shrinker, homeomorphic to the sphere, immersed in the three dimensional Euclidean space is a round sphere, provided its mean cur…