arXiv subjects
Publications and source records attributed to Ronggang Li.
We prove that the critical value $2π^2$ is isolated for the Möbius cross energy of two-component links in the round three dimensional sphere $\mathbb{S}^{3}$. Specifically, there exists $\varepsilon_0>0$ such that any non-split, regular $H^2$ pair of curves with disjoint images, having vanishing first variation and energy at most $2π^2+\varepsilon_0$, must lie in the Möbius-reparametrization orbit of the standard Hopf link.
Let $(M^{n}, g)$ be a complete, simply connected Riemannian manifold without boundary, of dimension $n\ge3$, with curvature operator at least that of the unit sphere. We prove that $$\int_M {\rm scal}(x)\ d {\rm Vol}_x\le n(n-1)ω_n,$$ where $ω_n$ is the volume of the unit $n$-sphere. Equality holds if and only if $(M,g)$ is isometric to the unit round sphere. In fact, we obtain a stronger bound containing ${\rm Vol}(M, g)$. In even dimensions, the proof follows from the Chern-Gauss-Bonnet formula. In odd dimensions, we apply the corresponding boundary formula to Deruelle's Ricci expander filling.
Intraoperative pathology is pivotal to precision surgery, yet its clinical impact is constrained by diagnostic complexity and the limited availability of high-quality frozen-section data. While computational pathology has made significant strides, the lack of large-scale, prospective validation has impeded its routine adoption in surgical workflows. Here, we introduce CRISP, a clinical-grade foundation model developed on over 100,000 frozen sections from eight medical centers, specifically designed to provide Clinical-grade Robust Intraoperative Support for Pathology (CRISP). CRISP was comprehensively evaluated on more than 15,000 intraoperative slides across nearly 100 retrospective diagnostic tasks, including benign-malignant discrimination, key intraoperative decision-making, and pan-cancer detection, etc. The model demonstrated robust generalization across diverse institutions, tumor types, and anatomical sites-including previously unseen sites and rare cancers. In a prospective cohort of over 2,000 patients, CRISP sustained high diagnostic accuracy under real-world conditions, directly informing surgical decisions in 92.6% of cases. Human-AI collaboration further reduced diagnostic workload by 35%, avoided 105 ancillary tests and enhanced detection of micrometastases with 87.5% accuracy. Together, these findings position CRISP as a clinical-grade paradigm for AI-driven intraoperative pathology, bridging computational advances with surgical precision and accelerating the translation of artificial intelligence into routine clinical practice.
In this paper, we present extensions of the classical Bonnet-Myers theorem for Riemannian manifolds with nonnegative Ricci curvature. Our results provide criteria for compactness and a method for estimating the diameter of such manifolds under general curvature conditions. As applications, we establish compactness theorems for manifolds whose Ricci curvature decays at polynomial or exponential rates.
In this note, we study the radius of positively curved or non-negatively curved Alexandrov space with strictly convex boundary, with convexity measured by the Base-Angle defined by Alexander and Bishop. We also estimate the volume of the boundary of non-negatively curved spaces as well as the rigidity case, which can be thought as a non-negatively curved version of a recent result of Grove-Petersen.
Inspired by a recent work of Grove-Petersen in [GP18], where the authors studied Alexandrov spaces with largest possible boundary. We study Alexandrov spaces with lower curvature bound 1 and with small boundary. When the radius of X is π/2, and the boundary has diameter π/2, we classify the total space X.