One of the main results of a recent paper by Gross–Tosatti–Zhang establishes estimates on the collapsing of Ricci-flat K¨ahler metrics on holomorphic torus fibrations. We remove a projectivity assumption from these estimates and simplify some of the underlying analysis.

We generalize the Gleason–Kahane–Z˙ elazko theorem to modules. As an application, we show that every linear functional on a Hardy space that is non-zero on the outer functions is a multiple of a point evaluation. A further consequence is that every linear endomorphism of a Hardy space that maps outer functions to nowhere-zero functions is a weighted composition operator. In neither cas…

Recently it was shown by H. Guenancia and M. P˘aun that a singular metric satisfying the conical K¨ahler–Einstein equation with a simple normal crossing divisor is quasi-isometric to a conical metric along that divisor. In this article, we present an alternative proof of their theorem.

We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With the goal of providing a complete self-contained proof, details surrounding map covariant derivatives and a careful application of the DeTurck trick are provided.

We generalize theorems of Cochran–Lickorish and Owens–Strle to the case of links with more than one component. This enables the use of linking forms on double branched covers, Heegaard Floer correction terms, and Donaldson’s diagonalization theorem to complete the table of unlinking numbers for nonsplit prime links with crossing number nine or less.

We describe the spectrum of certain integration operators acting on generalized Fock spaces.

Given any ε > 0, we construct an orthonormal system of nk uniformly bounded polynomials of degree at most k on the unit sphere in Rm+1 where nk is bigger than 1 − ε times the dimension of the space of polynomials of degree at most k. Similarly, we construct an orthonormal system of sections of powers Ak of a positive holomorphic line bundle on a compact K¨ahler manifold with ca…

We show that the complement of the closure of the coamoeba of a variety of codimension k + 1 is k-convex, in the sense of Gromov and Henriques. This generalizes a result of Nisse for hypersurface coamoebas. We use this to show that the complement of the nonarchimedean coamoeba of a variety of codimension k + 1 is k-convex.

Using the Bockstein spectral sequence developed previously by the authors, we compute the ring ER(n)∗(BO(q)) explicitly. We then use this calculation to show that the ring spectrum MO[2n+1] is ER(n)-orientable (but not ER(n + 1)-orientable), where MO[2n+1] is defined as the Thom spectrum for the self-map of BO given by multiplication by 2n+1.

Let d > 1 be an integer. In 1986, Shen defined a class of weight modules Fα b (V) over the Witt algebra Wd for α ∈ Cd, b ∈ C, and an irreducible module V over the general linear Lie algebra gld on which the identity matrix acts as multiplication by b. In 1996, Eswara Rao determined necessary and sufficient conditions for these modules to be irreducible when V is finite-dim…