arXiv research

Estimates for scalar curvature equations on Kähler manifolds with singularities.

Estimates for metrics with constant Chern scalar curvature on complex manifolds.

The paper provides estimates for Kähler metrics with constant scalar curvature.

In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota's argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of…

Proves curvature estimates for 3D surfaces solving scalar curvature equations.

Paper refines Chen-Cheng's estimates for Kähler metrics.

Establishes interior C2 estimates for convex solutions to curvature equations.

Upper diameter bound for manifolds with positive scalar curvature.

This note relaxes conditions for Kähler metrics with bounded entropy and scalar curvature.

Estimates scalar curvature of point clouds without embedding.

Estimates scalar curvature on moduli space as genus grows.

Study of charged scalar fields on Reissner-Nordström spacetimes via energy estimates.

This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature. We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some nonexistence results for complete solutions of scalar curvature equation.

New decay estimates for scalar curvature of steady gradient Ricci solitons.

The paper establishes distance estimates for manifolds with lower scalar curvature bounds.

Study on gradient h-almost Yamabe solitons with scalar curvature estimation.

Estimates scalar curvature without nonnegativity, showing gap phenomenon on manifolds.

Estimates mean curvature, scalar curvature, shape operator in warped products.

Sharp curvature estimates for expanding Ricci solitons in various dimensions.

Paper proves estimates for metrics with conic singularities.

The paper improves curvature estimates for Ricci flow solutions with bounded scalar curvature.

New proof for curvature and diameter estimates on Fano manifolds.

Upper bound found for systolic geometry on manifolds with positive scalar curvature.

The paper estimates distances between manifold boundaries based on scalar curvature.

Second part of series studying charged scalar fields on Reissner--Nordström spacetimes.

Study on 3-manifolds with nonnegative scalar curvature and positive harmonic functions.

Sharp estimate for 2-systole on Kähler surfaces with positive scalar curvature.

Second paper in series solves Einstein vacuum equations for three impulsive waves.

Paper examines conditions making Riemann solitons trivial and estimates their scalar curvature.

Study on positive scalar curvature and its impact on Ricci limit spaces.

On Riemannian manifolds of dimension 4, for prescribed scalar curvature equation, under lipschitzian condition on the prescribed curvature, we have an uniform estimate for the solutions of the equation if we control their minimas.

Upper estimate of Dirac eigenvalue linked to hyperspherical radius.

The paper explores geometry and positive scalar curvature on non-compact manifolds.

We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove that the flow converges to a spacel…

The paper characterizes solitons and estimates scalar curvature.

Study pinches curvature under Laplacian G_2 flow, proving Weyl tensor norm blows up.

We obtain a priori estimates for solutions to the prescribed scalar curvature equation on $S^3$. The usual non-degeneracy assumption on the curvature function is replaced by a new condition, which is necessary and sufficient for the existence of a priori estimates, when the curvature function is a positive Morse functi…

Uniform distance distortion estimate for Ricci flows with bounded scalar curvature.

The paper proves estimates for Hermitian metrics and shows curvature blow-up on complex manifolds.

Sharp gradient estimate for scalar curvature on 3-manifolds.

The study explores positive scalar curvature metrics on non-orientable manifolds and their covers.

The study examines how average scalar curvature influences geometric properties of Riemannian manifolds.

Estimates on Dirac operator eigenvalues for reducible manifolds.

The paper extends Gromov's K-cowaist to complete foliated manifolds and estimates leafwise scalar curvature.

In this paper, we first derive a pinching estimate on the traceless Ricci curvature in term of scalar curvature and Weyl tensor under the Ricci flow. Then we apply this estimate to study finite-time singularity behavior. We show that if the scalar curvature is uniformly bounded, then the Weyl tensor has to blow up, as …

Developing a singular dimension descent method for positive scalar curvature obstructions

The paper proves a quantitative positive mass theorem for spin manifolds with distance estimates.

It has recently been conjectured that the eigenvalues $λ$ of the Dirac operator on a closed Riemannian spin manifold $M$ of dimension $n\ge 3$ can be estimated from below by the total scalar curvature: $λ^2 \ge \frac{n}{4(n-1)} \cdot \frac{\int_M S}{vol(M)}.$ We show by example that such an estimate is impossible.