期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2021; 118 (1)
In [HLY1], Hosono, Lian, and Yau gave a conjectural characterization of the set of solutions to certain Gelfand-Kapranov-Zelevinsky hypergeometric equ......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2021; 118 (3)
Let E-tau := (C/(Z + Z tau) be a flat torus and G(z; tau) be the Green function on E-tau. Consider the multiple Green function G(n) on (E-tau)(n): G(n......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2021; 118 (3)
In 1960s, Almgren [3, 4] initiated a program to find minimal hypersurfaces in Riemannian manifolds using min-max method. This program was largely adva......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2021; 118 (3)
The wedge product on de Rham complex of a Riemannian manifold M can be pulled back to H*(M) via explicit homotopy constructed by using Green's operato......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2020; 115 (2)
Associated with isoparametric foliations of unit spheres, there are two classes of minimal surfaces minimal isoparametric hypersurfaces and focal subm......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2020; 115 (2)
Let R = C[x(1),x(2), . . . ,x(n)]/(f) where f is a weighted homogeneous polynomial defining an isolated singularity at the origin. Then R and Der (R,R......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2020; 115 (3)
In this work, we obtain existence criteria for Chern-Ricci flows on noncompact manifolds. We generalize a result by Tossati-Wienkove [37] on Chern-Ric......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2020; 115 (3)
Finite dimensional Lie algebras are semi-direct product of the semisimple Lie algebras and solvable Lie algebras. Brieskorn gave the connection betwee......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2020; 116 (3)
Existence and uniqueness of the solution to the L-p Minkowski problem for the electrostatic p-capacity are proved when p > 1 and 1 < p < n. T......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2020; 116 (3)
By employing the Green function, in this paper we provide a new and elementary proof for the interior regularity of solutions to the Monge-Ampere equa......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2020; 114 (2)
It is well-known that the PDE (Partial Differential Equation) system arising from the infinitesimal Pluucker formulas is a particular case of the Toda......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2020; 114 (2)
We study Le Potier's strange duality conjecture on a rational surface. We focus on the case involving the moduli space of rank 2 sheaves with trivial ......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2020; 114 (2)
In this paper, we discuss the Weyl problem in warped product spaces. We apply the method of continuity and prove the openness of the Weyl problem. A c......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2019; 111 (1)
For n-dimensional central affine curve flows, we 1) solve the Cauchy problem with periodic initial data and with initial data having rapidly decaying ......
期刊： JOURNAL OF DIFFERENTIAL GEOMETRY, 2019; 111 (1)
Conformal invariance of two-dimensional variational problems is a condition known to enable a blow-up analysis of solutions and to deduce the removabi......
