Publications (54)
A Liouville theorem on asymptotically Calabi spaces
Song Sun, Ruobing Zhang
In this paper, we will study harmonic functions on the complete and incomplete spaces with nonnegative Ricci curvature which exhibit inhomogeneous collapsing behaviors at infinity.…
Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces
Hans-Joachim Hein, Song Sun, Jeff Viaclovsky +1
We exhibit families of Ricci-flat Kahler metrics on K3 surfaces which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding con…
Kahler-Einstein metrics and stability
Xiu-Xiong Chen, Simon Donaldson, Song Sun
We annnounce a proof of the fact that a K-stable Fano manifold admits a Kahler-Einstein metric and give a brief outline of the proof.
Testing log K-stability by blowing up formalism
Yuji Odaka, Song Sun
We study logarithmic K-stability for pairs by extending the formula for Donaldson-Futaki invariants to log setting. We also provide algebro-geometric counterparts of recent results…
Space of Kähler metrics (V)-- Kähler quantization
Xiuxiong Chen, Song Sun
We prove the convergence of geodesic distance during the quantization of the space of Kähler potentials. As applications, this provides alternative proofs of certain inequalities…
An infinite dimensional balanced embedding problem I:existence
Jingzhou Sun, Song Sun
We investigate the problem of balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. In this paper we prove the existence of such an em…
Reflexive sheaves, Hermitian-Yang-Mills connections, and tangent cones
Xuemiao Chen, Song Sun
In this paper we give a complete algebro-geometric characterization of analytic tangent cones of admissible Hermitian-Yang-Mills connections over any reflexive sheaves.
The generalized Frankel conjecture in Sasaki geometry
Weiyong He, Song Sun
We prove some structure results for \emph{transverse reducible} Sasaki manifolds. In particular, we show Sasaki manifolds with positive Ricci curvature is transversely irreducible,…
Algebraic tangent cones of reflexive sheaves
Xuemiao Chen, Song Sun
We study the notion of algebraic tangent cones at singularities of reflexive sheaves. These correspond to extensions of reflexive sheaves across a negative divisor. We show the exi…
Bionic Optical Physical Unclonable Functions for Authentication and Encryption
Yongbiao Wan, Pidong Wang, Feng Huang +9
Information security is of great importance for modern society with all things connected. Physical unclonable function (PUF) as a promising hardware primitive has been intensively…
Calabi flow, Geodesic rays, and uniqueness of constant scalar curvature Kähler metrics
Xiuxiong Chen, Song Sun
We prove that constant scalar curvature Kähler metric "adjacent" to a fixed Kähler class is unique up to isomorphism. This extends the uniqueness theorem of Donaldson and Chen-Ti…
Compact Moduli Spaces of Del Pezzo Surfaces and Kähler-Einstein metrics
Yuji Odaka, Cristiano Spotti, Song Sun
We prove that the Gromov-Hausdorff compactification of the moduli space of Kahler-Einstein Del Pezzo surfaces in each degree agrees with certain algebro-geometric compactification.…
Kähler-Ricci shrinkers and Fano fibrations
Song Sun, Junsheng Zhang
In this paper, we build connections between Kähler-Ricci shrinkers, i.e., complete (possibly non-compact) shrinking gradient Kähler-Ricci solitons, and algebraic geometry. In par…
Asymptotically Calabi metrics and weak Fano manifolds
Hans-Joachim Hein, Song Sun, Jeff Viaclovsky +1
We show that any asymptotically Calabi manifold which is Calabi-Yau can be compactified complex analytically to a weak Fano manifold. Furthermore, the Calabi-Yau structure arises f…
Singularities of Hermitian-Yang-Mills connections and Harder-Narasimhan-Seshadri filtrations
Xuemiao Chen, Song Sun
This is the first of a series of papers where we relate tangent cones of Hermitian-Yang-Mills connections at an isolated singularity to the complex algebraic geometry of the underl…
Anomalous Nernst effect induced terahertz emission in a single ferromagnetic film
Zheng Feng, Wei Tan, Zuanming Jin +17
By developing a bidirectional-pump terahertz (THz) emission spectroscopy, we reveal an anomalous Nernst effect (ANE) induced THz emission in a single ferromagnetic film. Based on t…
On conical asymptotically flat manifolds
Mingyang Li, Song Sun
We prove a conjecture of Petrunin and Tuschmann on the non-existence of asymptotically flat 4-manifolds asymptotic to the half plane. We also survey recent progress and questions c…
Explicit Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds
Cristiano Spotti, Song Sun
We exhibit the first non-trivial concrete examples of Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds in all complex dimensions bigger than t…
Classification results for expanding and shrinking gradient Kähler-Ricci solitons
Ronan J. Conlon, Alix Deruelle, Song Sun
We first show that a Kähler cone appears as the tangent cone of a complete expanding gradient Kähler-Ricci soliton with quadratic curvature decay with derivatives if and only if…
From almost smooth spaces to RCD spaces
Shouhei Honda, Song Sun
We provide various characterizations for a given almost smooth space to be an RCD space, in terms of a local volume doubling and a local Poincaré inequality. Applications include…
First principle calculation of the effective Zeeman's couplings in topological materials
Zhi-Da Song, Song Sun, Yuan-Feng Xu +4
In this paper, we propose a first principle calculation method for the effective Zeeman's coupling based on the second perturbation theory and apply it to a few topological materia…
VASP2KP: kp models and Lande g-factors from ab initio calculations
Sheng Zhang, Haohao Sheng, Zhi-Da Song +8
The method is significant in condensed matter physics for the compact and analytical Hamiltonian. In the presence of magnetic field, it is described by the effective Zee…
Unprotected quadratic band crossing points and quantum anomalous Hall effect in FeB2 monolayer
Dongyu Wu, Yunpeng Huang, Song Sun +6
Quadratic band crossing points (QBCPs) and quantum anomalous Hall effect (QAHE) have attracted the attention of both theoretical and experimental researchers in recent years. Based…
On the local topology of non-collapsed Ricci bounded limit spaces
Song Sun, Jikang Wang, Junsheng Zhang
We show that for a pointed Gromov-Hausdorff limit of non-collapsed Riemannian manifolds with bounded Ricci curvature, the local of the regular loci vanishes. We also discuss…
Collapsing geometry of hyperkähler 4-manifolds and applications
Song Sun, Ruobing Zhang
We investigate the collapsing geometry of hyperkähler 4-manifolds. As applications we prove two well-known conjectures in the field. (1) Any collapsed limit of unit-diameter hyper…
Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry
Simon Donaldson, Song Sun
We prove a general result about the geometry of holomorphic line bundles over Kahler manifolds.
Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 Ï
Xiuxiong Chen, Simon Donaldson, Song Sun
This is the second of a series of three papers which provide proofs of results announced in arXiv:1210.7494. In this paper we consider the Gromov-Hausdorff limits of metrics with c…
Note on geodesic rays tamed by simple test configurations
Song Sun
In this short note, we give a new proof of a theorem of Arezzo-Tian on the existence of smooth geodesic rays tamed by a special degeneration.
Generation of nearly pure and highly directional magnetic light in fluorescence of rare earth ions
Anton D. Utyushev, Roman Gaponenko, Song Sun +3
A thorough analysis of the emission via the magnetic dipole (MD) transition, called magnetic light below, of trivalent rare-earth ions in or near dielectric homogeneous spheres has…
Frankel Conjecture and Sasaki geometry
Weiyong He, Song Sun
We classify simply connected compact Sasaki manifolds of dimension with positive transverse bisectional curvature. In particular, the Kähler cone corresponding to such mani…
Geometry of gravitational instantons
Mingyang Li, Song Sun
We survey recent progress in the classification of hyperkähler and Hermitian gravitational instantons (i.e., complete noncompact 4 dimensional Ricci-flat manifolds with quadratic…
Existence and deformations of Kahler-Einstein metrics on smoothable Q-Fano varieties
Cristiano Spotti, Song Sun, Chengjian Yao
We prove the existence of Kahler-Einstein metrics on Q-Gorenstein smoothable, K-polystable Q-Fano varieties, and we show how these metrics behave, in the Gromov-Hausdorff sense, un…
On the Kähler-Ricci flow near a Kähler-Einstein metric
Song Sun, Yuanqi Wang
On a Fano manifold, we prove that the Kahler-Ricci flow starting from a Kahler metric in the anti-canonical class which is sufficiently close to a Kahler-Einstein metric must conve…
Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
Simon Donaldson, Song Sun
In this paper we continue to study Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry. Our main focus is on the algebro-geometric meaning of Riemannian tangent cone…
Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2Ï and completion of the main proof
Xiuxiong Chen, Simon Donaldson, Song Sun
This is the third and final paper in a series which establish results announced in arXiv:1210.7494. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singu…
Calabi-Yau manifolds with isolated conical singularities
Hans-Joachim Hein, Song Sun
Let be a complex projective variety with only canonical singularities and with trivial canonical bundle. Let be an ample line bundle on . Assume that the pair is…
Analytic tangent cones of admissible Hermitian-Yang-Mills connections
Xuemiao Chen, Song Sun
In this paper we study the analytic tangent cones of admissible Hermitian-Yang-Mills connections near a homogeneous singularity of a reflexive sheaf, and relate it to the Harder-Na…
Authentication of optical physical unclonable functions based on single-pixel detection
Pidong Wang, Feiliang Chen, Dong Li +8
Physical unclonable function (PUF) has been proposed as a promising and trustworthy solution to a variety of cryptographic applications. Here we propose a non-imaging based authent…
A note on Kähler-Ricci soliton
Xiuxiong Chen, Song Sun, Gang Tian
In this note we provide a proof of the following: Any compact KRS with positive bisectional curvature is biholomorphic to the complex projective space. As a corollary, we obtain an…
On the generalized numerical criterion
Sean Timothy Paul, Song Sun, Junsheng Zhang
In this note, we give examples that demonstrate a negative answer to the generalized numerical criterion problem for pairs.
Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities
Xiu-Xiong Chen, Simon Donaldson, Song Sun
This is the first of a series of three papers which provide proofs of results announced recently in arXiv:1210.7494.
Complex structure degenerations and collapsing of Calabi-Yau metrics
Song Sun, Ruobing Zhang
In this paper, we make progress on understanding the collapsing behavior of Calabi-Yau metrics on a degenerating family of polarized Calabi-Yau manifolds. In the case of a family o…
No semistability at infinity for Calabi-Yau metrics asymptotic to cones
Song Sun, Junsheng Zhang
We discover a "no semistability at infinity" phenomenon for complete Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance of an intermediate K-semistable…
Bubbling of Kähler-Einstein metrics
Song Sun
We prove the finite step termination of bubble trees for singularity formation of polarized Kähler-Einstein metrics in the non-collapsing situation. We also raise several question…
Excess-noise suppression for a squeezed state propagating through random amplifying media via wave-front shaping
Dong Li, Song Sun, Yao Yao
After propagating through a random amplifying medium, a squeezed state commonly shows excess noise above the shot-noise level. Since large noise can significantly reduce the signal…
Kähler-Ricci flow, Kähler-Einstein metric, and K-stability
Xiuxiong Chen, Song Sun, Bing Wang
We prove the existence of Kahler-Einstein metric on a K-stable Fano manifold using the recent compactness result on Kahler-Ricci flows. The key ingredient is an algebro-geometric d…
Strain-tuned topological phase transition and unconventional Zeeman effect in ZrTe5 microcrystals
Apurva Gaikwad, Song Sun, Peipei Wang +4
The geometric phase (Berry phase) of an electronic wave function is the fundamental basis of the topological properties in solids. Modulating band structure provides a tuning knob…
Projective embedding of log Riemann surfaces and K-stability
Jingzhou Sun, Song Sun
Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defi…
Note on K-stability of pairs
Song Sun
We prove that a pair (X, D) with X Fano and D a smooth anti-canonical divisor is K-unstable for negative angles, and K-semistable for zero angle.
The critical role of shell in enhanced fluorescence of metal-dielectric core-shell nanoparticles
Song Sun, Ilia L. Rasskazov, P. Scott Carney +2
Large scale simulations are performed by means of the transfer-matrix method to reveal optimal conditions for metal-dielectric core-shell particles to induce the largest fluorescen…
Gravitational instantons and harmonic maps
Mingyang Li, Song Sun
We study the interaction between toric Ricci-flat metrics in dimension 4 and axisymmetric harmonic maps from the 3-dimensional Euclidean space into the hyperbolic plane. Applicatio…
Conical Kahler-Einstein metric revisited
Chi Li, Song Sun
In this paper we introduce the "interpolation-degneration" strategy to study Kahler-Einstein metrics on a smooth Fano manifold with cone singularities along a smooth divisor that i…
Topological metals induced by Zeeman effect
Song Sun, Zhida Song, Hongming Weng +1
In the present paper, we propose a new way to classify centrosymmetric metals by studying the Zeeman effect caused by an external magnetic field described by the momentum dependent…
Quantized and half-quantized Anomalous Hall effect induced by in-plane magnetic field
Song Sun, Hongming Weng, Xi Dai
In this paper we propose that, quantized and nearly half-quantized intrinsic anomalous Hall effect can be induced by in-plane external magnetic field through the Zeeman coupling in…