66 citations · 176 across the 46 of their papers we have counts for
56 papers · 1 filter
Poisson K-stability and the semiclassical Yau--Tian--Donaldson correspondence
Vestislav Apostolov, Brent Pym, Jeffrey Streets
We introduce a notion of K-polystability for compact Kähler holomorphic Poisson manifolds. On the one hand, this notion of stability is well-adapted to constructions of moduli spac…
Toric geometry of generalized Kähler-Ricci solitons
Vestislav Apostolov, Giuseppe Barbaro, Jeffrey Streets +1
We establish a local equivalence between toric steady Kähler-Ricci solitons and -type toric generalized Kähler-Ricci solitons (GKRS). Under natural global conditions we show thi…
Pluriclosed flow and the Hull-Strominger system
Mario Garcia-Fernandez, Raul Gonzalez Molina, Jeffrey Streets
We define a natural extension of pluriclosed flow aiming at constructing solutions of the Hull-Strominger system. We give several geometric formulations of this flow, which yield a…
Rigidity results for non-Kähler Calabi-Yau geometries on threefolds
Vestislav Apostolov, Giuseppe Barbaro, Kuan-Hui Lee +1
We derive a canonical symmetry reduction associated to a compact non-Kähler Bismut-Hermitian-Einstein manifold. In real dimension , the transverse geometry is conformally Kähler…
Formal structure of scalar curvature in generalized Kähler geometry
Vestislav Apostolov, Jeffrey Streets, Yury Ustinovskiy
Building on works of Boulanger and Goto, we show that Goto's scalar curvature is the moment map for an action of generalized Hamiltonian automorphisms of the associated Courant alg…
Ricci flow on Courant algebroids
Jeffrey Streets, Charles Strickland-Constable, Fridrich Valach
We develop a theory of Ricci flow for metrics on Courant algebroids which unifies and extends the analytic theory of various geometric flows, yielding a general tool for constructi…
Optimal Transport and Generalized Ricci Flow
Eva Kopfer, Jeffrey Streets
We prove results relating the theory of optimal transport and generalized Ricci flow. We define an adapted cost functional for measures using a solution of the associated dilaton f…
The Riemannian and symplectic geometry of the space of generalized Kähler structures
Vestislav Apostolov, Jeffrey Streets, Yury Ustinovskiy
On a compact complex manifold endowed with a holomorphic Poisson tensor and a deRham class , we study the space of generalized Kähler (GK) st…
The generalized Kähler Calabi-Yau problem
Vestislav Apostolov, Xin Fu, Jeffrey Streets +1
We formulate an extension of the Calabi conjecture to the setting of generalized Kähler geometry. We show a transgression formula for the Bismut Ricci curvature in this setting, wh…
Scalar curvature, entropy, and generalized Ricci flow
Jeffrey Streets
We derive a family of weighted scalar curvature monotonicity formulas for generalized Ricci flow, involving an auxiliary dilaton field evolving by a certain reaction-diffusion equa…
Bochner formulas, functional inequalities and generalized Ricci flow
Eva Kopfer, Jeffrey Streets
As a consequence of the Bochner formula for the Bismut connection acting on gradients, we show sharp universal Poincaré and log-Sobolev inequalities along solutions to generalized…
Kähler stability of symplectic forms
Jeffrey Streets, Gang Tian
Using dynamical stability of symplectic curvature flow, we show that on a compact Calabi-Yau manifold, any small symplectic deformation of a Kähler form remains Kähler.
Variational structure and uniqueness of generalized Kähler-Ricci solitons
Vestislav Apostolov, Jeffrey Streets, Yury Ustinovskiy
Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system. We realize solutions as critical points of a functional analogous to the classic…
Four-dimensional generalized Ricci flows with nilpotent symmetry
Steven Gindi, Jeffrey Streets
We study solutions to generalized Ricci flow on four-manifolds with a nilpotent, codimension symmetry. We show that all such flows are immortal, and satisfy type III curvature…
Codimension four regularity of generalized Einstein structures
Xin Fu, Aaron Naber, Jeffrey Streets
We establish codimension 4 regularity of noncollapsed sequences of metrics with bounds on natural generalizations of the Ricci tensor. We obtain a priori L2 curvature estimates on…
Non-Kähler Calabi-Yau geometry and pluriclosed flow
Mario Garcia-Fernandez, Joshua Jordan, Jeffrey Streets
Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a natural extension of Calabi-Yau metrics to the setting of complex, non-Kähler manifolds, and arise independen…
Ricci-Yang-Mills flow on surfaces and pluriclosed flow on elliptic fibrations
Jeffrey Streets
We give a complete description of the global existence and convergence for the Ricci-Yang-Mills flow on bundles over Riemann surfaces. These results equivalently describe sol…
The Gibbons-Hawking ansatz in generalized Kähler geometry
Jeffrey Streets, Yury Ustinovskiy
We derive a local ansatz for generalized Kähler surfaces with nondegenerate Poisson structure and a biholomorphic action which generalizes the classic Gibbons-Hawking ansatz…
Generalized Ricci Flow
Mario Garcia-Fernandez, Jeffrey Streets
This book gives an introduction to fundamental aspects of generalized Riemannian, complex, and Kähler geometry. This leads to an extension of the classical Einstein-Hilbert action,…
Deformation classes in generalized Kähler geometry
Matthew Gibson, Jeffrey Streets
We introduce natural deformation classes of generalized Kähler structures using the Courant symmetry group. We show that these yield natural extensions of the notions of Kähler cla…
On a Calabi-type estimate for pluriclosed flow
Joshua Jordan, Jeffrey Streets
The regularity theory for pluriclosed flow hinges on obtaining regularity for the metric assuming uniform equivalence to a background metric. This estimate was established in…
Classification of generalized Kähler-Ricci solitons on complex surfaces
Jeffrey Streets, Yury Ustinovskiy
Using toric geometry we give an explicit construction of the compact steady solitons for pluriclosed flow first constructed in arXiv:1802.00170. This construction also reveals that…
Complex manifolds with negative curvature operator
Man-Chun Lee, Jeffrey Streets
We prove that compact complex manifolds with admitting metrics with negative Chern curvature operator either admit a -exact positive (1,1) current, or are Kähler with ample c…
Index-energy estimates for Yang-Mills connections and Einstein metrics
Matthew J. Gursky, Casey Lynn Kelleher, Jeffrey Streets
We prove a conformally invariant estimate for the index of Schrödinger operators acting on vector bundles over four-manifolds, related to the classical Cwikel-Lieb-Rozenblum estima…