23 citations · 122 across the 17 of their papers we have counts for
20 papers
Kähler Gradient Ricci Solitons with Large Symmetry
Hung Tran
Let be an irreducible non-trivial Kähler gradient Ricci soliton of real dimension . We show that its group of isometries is of dimension at most and the ca…
Rigidity of four-dimensional Kähler-Ricci solitons
Xiaodong Cao, Ernani Ribeiro, Hung Tran
In this article, we investigate four-dimensional gradient shrinking Ricci solitons close to a Kähler model. The first theorem could be considered as a rigidity result for the Kähle…
Curvature of the Second kind and a conjecture of Nishikawa
Matthew Gursky, Xiaodong Cao, Hung Tran
In this paper, we investigate manifolds for which the curvature of the second kind (following the terminology of Nishikawa) satisfies certain positivity conditions. Our main result…
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…
Stationary Surfaces with Boundaries
Anthony Gruber, Magdalena Toda, Hung Tran
This article investigates stationary surfaces with boundaries, which arise as the critical points of functionals dependent on curvature. Precisely, a generalized "bending energy" f…
On the variation of curvature functionals in space forms with application to a generalized Willmore energy
Anthony Gruber, Magdalena Toda, Hung Tran
Functionals involving surface curvature are important across a range of scientific disciplines, and their extrema are representative of physically meaningful objects such as atomic…
Four-manifolds of Pinched Sectional Curvature
Xiaodong Cao, Hung Tran
In this paper, we study closed four-dimensional manifolds. In particular, we show that under various new pinching curvature conditions (for example, the sectional curvature is no m…
The Gauss map of a free boundary minimal surface
Hung Tran
In this paper, we study the Gauss map of a free boundary minimal surface. The main theorem asserts that if components of the Gauss map are eigenfunctions of the Jacobi-Steklov oper…
On the Morse index of higher-dimensional free boundary minimal catenoids
Graham Smith, Ari Stern, Hung Tran +1
For all , we define the -dimensional critical catenoid to be the unique rotationally symmetric, free boundary minimal hypersurface of non-trivial topology embedded in t…
Einstein four-manifolds of pinched sectional curvature
Xiaodong Cao, Hung Tran
In this paper, we obtain classification of four-dimensional Einstein manifolds with positive Ricci curvature and pinched sectional curvature. In particular, the first result concer…
Index Characterization for Free Boundary Minimal Surfaces
Hung Tran
In this paper, we compute the Morse index for a free boundary minimal submanifold from data of two simpler problems. The first one is the corresponding problem with fixed boundary…
On Closed Manifolds with Harmonic Weyl Curvature
Hung Tran
We derive point-wise and integral rigidity/gap results for a closed manifold with harmonic Weyl curvature in any dimension. In particular, there is a generalization of Tachibana's…
Complete manifolds with bounded curvature and spectral gaps
Richard Schoen, Hung Tran
We study the spectrum of complete noncompact manifolds with bounded curvature and positive injectivity radius. We give general conditions which imply that their essential spectrum…
Harnack Estimates for Conjugate Heat Kernel on Evolving Manifolds
Xiaodong Cao, Hongxin Guo, Hung Tran
In this article we derive Harnack estimates for conjugate heat kernel in an abstract geometric flow. Our calculation involves a correction term D. When D is nonnegative, we are abl…
Partial regularity for minimizers of singular energy functionals, with application to liquid crystal models
Lawrence C. Evans, Olivier Kneuss, Hung Tran
We study the partial regularity of minimizers for certain singular functionals in the calculus of variations, motivated by Ball and Majumdar's recent modification [BM] of the Landa…
The Weyl Tensor of Gradient Ricci Solitons
Xiaodong Cao, Hung Tran
This paper derives new identities for the Weyl tensor on a gradient Ricci soliton, particularly in dimension four. First, we prove a Bochner-Weitzenböck type formula for the norm o…
Heat kernel estimates under the Ricci-Harmonic map flow
Mihai Băileşteanu, Hung Tran
The paper considers the Ricci flow, coupled with the harmonic map flow between two manifolds. We derive estimates for the fundamental solution of the corresponding conjugate heat e…
Mean Value Inequalities and Conditions to Extend Ricci Flow
Xiaodong Cao, Hung Tran
This paper concerns conditions related to the first finite singularity time of a Ricci flow solution on a closed manifold. In particular, we provide a systematic approach to the me…
Harnack Estimates for Ricci Flow on a Warped Product
Hung Tran
In this paper, we study the Ricci flow on closed manifolds equipped with warped product metric with Ricci flat. Using the framework of mon…