Related papers: Proof of the normal scalar curvature conjecture

We give a direct, purely arithmetical and elementary proof of the strong normalization of the cut-elimination procedure for full (i.e. in presence of all the usual connectives) classical natural deduction.

We give some classifications of biharmonic hypersurfaces with constant scalar curvature. These include biharmonic Einstein hypersurfaces in space forms, compact biharmonic hypersurfaces with constant scalar curvature in a sphere, and some…

A proof of Sendov's conjecture is given.

In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoids are equivariantly isomorphic. We also state and prove a uniqueness property for not necessarily smooth affine…

In this paper, assuming that a polarized algebraic manifold $(X,L)$ is strongly K-stable, we shall show that the polarization class $c_1(L)$ admits a constant scalar curvature Kaehler metric.

The Slope Conjecture relates the degree of the colored Jones polynomial of a knot to boundary slopes of incompressible surfaces. Our aim is to prove the Slope Conjecture for Montesinos knots, and to match parameters of a state-formula for…

In this paper, we prove that the static triple with half harmonic Weyl curvature and positive scalar curvature must be the standard hemisphere.

We prove the conjectures of Hodge and Tate for any six-dimensional hyper-K\"ahler variety that is deformation equivalent to a generalized Kummer variety.

In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds.

In this paper, we propose a generalization of a congruence due to Carlitz.

The first two authors introduced vertex distortion and showed that the vertex distortion of the unknot is trivial. It was conjectured that the vertex distortion of a knot is trivial if and only if the knot is trivial. We will use…

We observe what the canonical bundle formula gives towards a conjecture of Schnell on algebraic fiber spaces, a question concerning the equivalence between the non-vanishing conjecture and the Campana--Peternell conjecture. As a result, we…

We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.

Prescribed mean curvature problems on the torus has been considered in one dimension. In this paper, we prove the existence of a graph on the $n$-dimensional torus $\mathbb {T}^n$, the mean curvature vector of which equals the normal…

A one-line proof of a minimax theorem due to Steinerberger is given.

We prove that for $n>3$ each generic simple polytope in $\mathbb{R}^n$ contains a point with at least $2n+4$ emanating normals to the boundary. This result is a piecewise-linear counterpart of a long-standing problem about normals to smooth…

We prove a conjecture of Meszaros and Morales on the volume of a flow polytope. Independently from our work, Zeilberger sketched a proof of their conjecture. In fact, our proof is the same as Zeilberger's proof. The purpose of this note is…

This is the first in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global confor- mal invariants"; these are defined to be conformally invariant integrals of geometric scalars.…

As already noted by Niels Borne and Michel Emsalem, there is a natural generalization of the section conjecture for proper orbicurves. Combined with the reformulation by Niels Borne and Angelo Vistoli of the conjecture in terms of the…

This paper studies Cheeger deformations on $\mathrm{S}^3, \mathrm{SO}(3)$ principal bundles to obtain conditions for positive sectional curvature submersion metrics. We conclude, in particular, a stronger version of the Petersen--Wilhelm…