arXiv research

Study CR Yamabe constant and CR structures on manifolds.

Study CR Yamabe constant, flow, and soliton on CR manifolds.

We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular we show that the Yamabe constant depends continuously on the Riemannian metric with respect to the fine C^2-topology, and that the Yamabe…

Study on $G$-equivariant second Yamabe constant for manifolds.

The study compares and finds Yamabe constants on warped products.

Connected sum of CR manifolds with positive CR Yamabe constant is possible.

Connected sum of CR manifolds preserves positive CR Yamabe constant.

Paper shows k-Yamabe solitons have constant curvature under certain conditions.

Study convergence of Yamabe flow on singular spaces with positive constant.

The paper finds conditions for Yamabe solitons' metrics to be constant scalar curvature.

The Yamabe flow converges to a specific function on compactified manifolds.

Study shows long-term flow on special manifolds with positive Yamabe constant.

Paper finds conditions for non-Einstein relative Yamabe metrics.

For a closed Riemannian manifold $(M^m,g)$ of constant positive scalar curvature and any other closed Riemannian manifold $(N^n,h)$, we show that the limit of the Yamabe constants of the Riemannian products $(M\times N,g+rh)$ as $r$ goes to infinity is equal to the Yamabe constant of $(M^m \times R^n, [g+g_E])$ and is …

Study finds nodal solutions of Yamabe equation constant along isoparametric levels.

Study on warped product Yamabe solitons with constant fiber curvature.

Let (V,g) and (W,h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V x W, g+h) in terms of the conformal Yamabe constants of (V,g) and (W,h).

Study on how relative Yamabe constant evolves under Ricci flow.

The paper classifies expanding gradient Yamabe solitons based on scalar curvature.

Paper shows constant σk-curvature for quasi k-Yamabe solitons.

The paper explores Yamabe solitons on specific types of 3D manifolds.

In the work of Ammann, Dahl and Humbert it has turned out that the Yamabe invariant on closed manifolds is a bordism invariant below a certain threshold constant. A similar result holds for a spinorial analogon. These threshold constants are characterized through Yamabe-type equations on products of spheres with rescal…

The study proves rotationally symmetric property of certain shrinking gradient Yamabe solitons.

Proves product metrics are Yamabe metrics under small flat torus conditions.

New approach linking CR Yamabe invariant to Sasaki structures.

The paper proves gap theorems for Yang-Mills on manifolds with positive Yamabe.

Let $(M^m,g)$ be a closed Riemannian manifold $(m\geq 2)$ of positive scalar curvature and $(N^n,h)$ any closed manifold. We study the asymptotic behaviour of the second Yamabe constant and the second $N-$Yamabe constant of $(M\times N,g+th)$ as $t$ goes to $+\infty$. We obtain that $\lim_{t \to +\infty}Y^2(M\times N,[…

The study classifies specific types of solitons with bounded scalar curvature.

The paper proves solutions for Yamabe equations on manifolds with boundary.

Characterizes gradient Yamabe solitons with specific conditions.

We study a particular class of open manifolds. In the category of Riemannian manifolds these are complete manifolds with cylindrical ends. We give a natural setting for the conformal geometry on such manifolds including an appropriate notion of the cylindrical Yamabe constant/invariant. This leads to a corresponding ve…

Conditions for trivial gradient hyperbolic Ricci and Yamabe solitons to be Einstein or constant scalar curvature.

The Chern-Yamabe flow solves curvature problems on specific manifolds.

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non homothetic solutions of the Yamabe problem. Using local rigi…

Study on Yamabe problem with potential in Euclidean space.

The paper studies ball packings on 3-manifolds and introduces a combinatorial Yamabe invariant.

New iterative method solves Yamabe problem on small domains.

New local method solves Yamabe problems on compact and non-compact manifolds.

Solution to qc Yamabe problem on non-spherical quaternionic contact manifolds.

The paper studies geometric properties of Yamabe solitons on compact manifolds.

The paper defines and analyzes a new mass function for compact manifolds.

Study finds multiple constant curvature metrics in product spaces.

In this note under a crucial technical assumption we derive a differential equality of the Yamabe constant $\mathcal{Y} (g (t))$ where $g (t)$ is a solution of the Ricci flow on a closed manifold.

The paper revisits the $σ_k$-Yamabe problem and proves the existence of a conformal metric with constant $σ_2$-scalar curvature.

We estimate from below the isoperimetric profile of $S^2 \times \re^2$ and use this information to obtain lower bounds for the Yamabe constant of $S^2 \times \re^2$. This provides a lower bound for the Yamabe invariants of products $S^2 \times M^2$ for any closed Riemann surface $M$. Explicitly we show that $Y(S^2 \tim…

Given closed Riemannian manifold $(M^n, g)$ of positive Ricci curvature $Ricci(g) \geq (n-1)g$ we study isoperimetric regions on the spherical cone over $M$. When $g$ is Einstein we use this to compute the Yamabe constant of $(M \times {\bf R}, g + dt^2)$ and so to obtain lower bounds for the Yamabe invariant of $M\tim…

The study proves CR structures on specific three-manifolds are equivalent to standard structures.

Study Cheeger constant and Yamabe type for ALH manifolds.