arXiv subjects
Publications and source records attributed to Junlong Yu.
In this paper, we study the complete gradient Ricci solitons $(M^n, g,f)$ with zero radial Weyl curvature, which means that the interior product of $\nabla f$ with the Weyl tensor $W$ is zero, i.e., $i_{\nabla f}W=0$. We classify completely the complete gradient Ricci solitons with zero radial Weyl curvature for the dimension $n\geq 4$.
A critical point metric is a critical point of the total scalar curvature functional restricted to the space of constant scalar curvature metrics on a closed manifold with unit volume. It was conjectured in 1980's that every critical point metric must be Einstein. In this paper, we prove that this conjecture is true if the norm of the traceless Ricci operator $|\widetilde{Ric}|$ is constant. For $3$-dimensional case, we prove that the conjecture is true, if the traceless Ricci operator satisfies $tr((\widetilde{Ric})^3)\geq -\frac{R}{12}|\widetilde{Ric}|^2$, where $R$ denotes the scalar curvature. where R denotes the scalar curvature.
This paper presents GaussEdit, a framework for adaptive 3D scene editing guided by text and image prompts. GaussEdit leverages 3D Gaussian Splatting as its backbone for scene representation, enabling convenient Region of Interest selection and efficient editing through a three-stage process. The first stage involves initializing the 3D Gaussians to ensure high-quality edits. The second stage employs an Adaptive Global-Local Optimization strategy to balance global scene coherence and detailed local edits and a category-guided regularization technique to alleviate the Janus problem. The final stage enhances the texture of the edited objects using a sophisticated image-to-image synthesis technique, ensuring that the results are visually realistic and align closely with the given prompts. Our experimental results demonstrate that GaussEdit surpasses existing methods in editing accuracy, visual fidelity, and processing speed. By successfully embedding user-specified concepts into 3D scenes, GaussEdit is a powerful tool for detailed and user-driven 3D scene editing, offering significant improvements over traditional methods.