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Yuxing Deng

Publications and source records attributed to Yuxing Deng.

16 recordsLinked to original sources
arXiv2026

Ancient Ricci flows with nonnegative Ricci curvature

In this paper, we study the asymptotic geometry of a noncollapsed ancient Ricci flow with nonnegative Ricci curvature via its tangent flow at infinity -- a noncollapsed $\mathbb{F}$-limit metric soliton [Bam23,CMZ23]. We first prove some estimates for noncollapsed $\mathbb{F}$-limit metric solitons with nonnegative Ricci curvature, and then obtain two dichotomy theorems for ancient Ricci flows. In particular, we show that: (1) for a noncollapsed ancient Ricci flow with nonnegative Ricci curvature, either its asymptotic volume ratio is always zero, or every tangent flow at infinity is a Ricci flat cone; (2) for a noncollapsed ancient Ricci flow with positively pinched Ricci curvature ($\operatorname{Ric}\ge \varepsilon R g$), either it is compact, or every tangent flow at infinity is a Ricci flat cone.

math.DG↗
arXiv2025

Rigidity of positively curved Steady gradient Ricci solitons on orbifolds

In this paper, we study gradient Ricci soitons on smooth orbifolds. We prove that the scalar curvature of a complete shrinking or steady gradient Ricci soliton on an orbifold is nonnegative. We also show that a complete $\kappa$-noncollapsed steady gradient Ricci soliton on a Riemannian orbifold with positive curvature operator, compact singularity and linear curvature decay must be a finite quotient of the Bryant soliton. Finally, we show that a complete steady gradient Ricci soliton on a Riemannian orbifold with positive sectional curvature must be a finite quotient of the Bryant soliton if it is asymptotically quotient cylindrical.

math.DG↗
arXiv2024

On the fundamental group of steady gradient Ricci solitons with nonnegative sectional curvature

In this paper, we study the fundamental group of the complete steady gradient Ricci soliton with nonnegative sectional curvature. We prove that the fundamental group of such a Ricci soliton is either trivial or infinite. As a corollary, we show that an $n$-dimensional complete $\kappa$-noncollapsed steady gradient Ricci soliton with nonnegative sectional curvature must be diffeomorphic to $\mathbb{R}^n$.

math.DG↗
arXiv2023

Incipient Fault Detection in Power Distribution System: A Time-Frequency Embedded Deep Learning Based Approach

Incipient fault detection in power distribution systems is crucial to improve the reliability of the grid. However, the non-stationary nature and the inadequacy of the training dataset due to the self-recovery of the incipient fault signal, make the incipient fault detection in power distribution systems a great challenge. In this paper, we focus on incipient fault detection in power distribution systems and address the above challenges. In particular, we propose an ADaptive Time-Frequency Memory(AD-TFM) cell by embedding wavelet transform into the Long Short-Term Memory (LSTM), to extract features in time and frequency domain from the non-stationary incipient fault signals.We make scale parameters and translation parameters of wavelet transform learnable to adapt to the dynamic input signals. Based on the stacked AD-TFM cells, we design a recurrent neural network with ATtention mechanism, named AD-TFM-AT model, to detect incipient fault with multi-resolution and multi-dimension analysis. In addition, we propose two data augmentation methods, namely phase switching and temporal sliding, to effectively enlarge the training datasets. Experimental results on two open datasets show that our proposed AD-TFM-AT model and data augmentation methods achieve state-of-the-art (SOTA) performance of incipient fault detection in power distribution system. We also disclose one used dataset logged at State Grid Corporation of China to facilitate future research.

eess.SP↗
arXiv2022

Autonomous Smart Grid Fault Detection

Smart grid plays a crucial role for the smart society and the upcoming carbon neutral society. Achieving autonomous smart grid fault detection is critical for smart grid system state awareness, maintenance and operation. This paper focuses on fault monitoring in smart grid and discusses the inherent technical challenges and solutions. In particular, we first present the basic principles of smart grid fault detection. Then, we explain the new requirements for autonomous smart grid fault detection, the technical challenges and their possible solutions. A case study is introduced, as a preliminary study for autonomous smart grid fault detection. In addition, we highlight relevant directions for future research.

cs.DC↗
arXiv2022

On Four-dimensional Steady gradient Ricci solitons that dimension reduce

In this paper, we will study the asymptotic geometry of 4-dimensional steady gradient Ricci solitons under the condition that they dimension reduce to $3$-manifolds. We will show that such 4-dimensional steady gradient Ricci solitons either dimension reduce to a spherical space form $\mathbb{S}^3/Γ$ or weakly dimension reduce to the $3$-dimensional Bryant soliton. We also show that 4-dimensional steady gradient Ricci soliton singularity models with nonnegative Ricci curvature outside a compact set either are Ricci-flat ALE $4$-manifolds or dimension reduce to $3$-dimensional manifolds. As an application, we prove that any steady gradient Kähler-Ricci soliton singularity models on complex surfaces with nonnegative Ricci curvature outside a compact set must be hyperkähler ALE Ricc-flat $4$-manifolds.

math.DG↗
arXiv2022

Four-Dimensional Steady Gradient Ricci Solitons with $3$-Cylindrical Tangent Flows at Infinity

In this paper we consider $4$-dimensional steady soliton singularity models, i.e., complete steady gradient Ricci solitons that arise as the rescaled limit of a finite time singular solution of the Ricci flow on a closed $4$-manifold. In particular, we study the geometry at infinity of such Ricci solitons under the assumption that their tangent flow at infinity is the product of $\mathbb{R}$ with a $3$-dimensional spherical space form. We also classify the tangent flows at infinity of $4$-dimensional steady soliton singularity models in general.

math.DG↗
arXiv2018

A note on compact $κ$-solutions of Kähler-Ricci flow

In this paper, we give a complete classification of $κ$-solutions of Kähaler-Ricci flow on compact complex manifolds. Namely, they must be quotients of products of irreducible compact Hermitian symmetric manifolds.

math.DG↗
arXiv2018

Classification of gradient steady Ricci solitons with linear curvature decay

In this paper, we give a description for steady Ricci solitons with a linear decay of sectional curvature. In particular, we classify all 3-dimensional steady Ricci solitons and 4-dimensional $κ$-noncollpased steady Ricci solitons with nonnegative sectional curvature under the linear curvature decay.

math.DG↗
arXiv2017

Asymptotic behavior of positively curved steady Ricci Solitons

In this paper, we analyze the asymptotic behavior of $κ$-noncollapsed and positively curved steady Ricci solitons and prove that any $n$-dimensional $κ$-noncollapsed steady Kähler-Ricci soliton with non-negative sectional curvature must be flat.

math.DG↗
arXiv2016

3d steady Gradient Ricci Solitons with linear curvature decay

In this note, we prove that a 3-dimensional steady Ricci soliton is rotationally symmetric if its scalar curvature $R(x)$ satisfies $$\frac{C_0^{-1}}{ρ(x)}\le R(x)\le \frac{C_0}{ρ(x)}$$ for some constant $C_0>0$, where $ρ(x)$ denotes the distance from a fixed point $x_0$. Our result doesn't assume that the soliton is $κ$-noncollapsed.

math.DG↗
arXiv2016

Steady Ricci solitons with horizontally $ε$-pinched Ricci curvature

In this paper, we prove that any $κ$-noncollapsed gradient steady Ricci soliton with nonnegative curvature operator and horizontally $ε$-pinched Ricci curvature must be rotationally symmetric. As an application, we show that any $κ$-noncollapsed gradient steady Ricci soliton $(M^n, g,f)$ with nonnegative curvature operator must be rotationally symmetric if it admits a unique equilibrium point and its scalar curvature $R(x)$ satisfies $\lim_{r(x)\rightarrow\infty}R(x)f(x)=C_0\sup_{x\in M}R(x)$ with $C_0>\frac{n-2}{2}$.

math.DG↗
arXiv2013

Complete non-compact gradient Ricci solitons with nonnegative Ricci curvature

In this paper, we give a delay estimate of scalar curvature for a complete non-compact expanding (or steady) gradient Ricci soliton with nonnegative Ricci curvature. As an application, we prove that any complete non-compact expanding (or steady) gradient Kähler-Ricci solitons with positively pinched Ricci curvature should be Ricci flat. The result answers a question in case of Kähler-Ricci solitons proposed by Chow, Lu and Ni in a book.

math.DG↗
arXiv2012

Characterisations of Testing Preorders for a Finite Probabilistic pi-Calculus

We consider two characterisations of the may and must testing preorders for a probabilistic extension of the finite pi-calculus: one based on notions of probabilistic weak simulations, and the other on a probabilistic extension of a fragment of Milner-Parrow-Walker modal logic for the pi-calculus. We base our notions of simulations on the similar concepts used in previous work for probabilistic CSP. However, unlike the case with CSP (or other non-value-passing calculi), there are several possible definitions of simulation for the probabilistic pi-calculus, which arise from different ways of scoping the name quantification. We show that in order to capture the testing preorders, one needs to use the "earliest" simulation relation (in analogy to the notion of early (bi)simulation in the non-probabilistic case). The key ideas in both characterisations are the notion of a "characteristic formula" of a probabilistic process, and the notion of a "characteristic test" for a formula. As in an earlier work on testing equivalence for the pi-calculus by Boreale and De Nicola, we extend the language of the $π$-calculus with a mismatch operator, without which the formulation of a characteristic test will not be possible.

cs.LO↗