9 problems

Rigidity conjecture. Any such solution $u$ must be a quadratic polynomial.

Green function rigidity conjecture. Then $(M,g)$ is a round sphere.

The paper considers the operators appearing in Theorem 2.1, acting at the level of equivariant $K$-theory. Rigidity conjecture. The operators considered in Theorem 2.1 are rigid on…

Let $X:M^n\to\mathbb{R}^{n+1}$ be a complete self-shrinker, and let $S$ be the squared norm of its second fundamental form. Cheng–Wei–Yano's conjecture. If $S$ is constant, then…

Let $(M,g)\in\mathcal{M}_{\rm Rc}(m)$, and let $(\widetilde M,\widetilde g)$ be its Riemannian universal covering. The quantitative space-form rigidity theorem concerns lower bound…

Almost-rigidity conjecture. A subsequence should converge intrinsically flatly to $M_0$, whose cover $\widetilde M_0$ is isometric to $\mathbb S^2\times\mathbb R$:

Conjecture 0.3. If $|X_1X_2|\geq\frac\pi2$ and $n_1+n_2=n-2$, then either the $X_i$ belong to a compact convex subset of dimension $n-1$ in $X$, or $X$ is isometric to a spherical…

Let $M^n$, with $n\geq4$, be an even-dimensional compact and simply connected Riemannian manifold. Let $K_M$ denote the curvature quantity used in the source, let $R_0$ be the norm…

Let $M^n$ be a compact and simply connected Riemannian manifold. Let $K_M$ denote the relevant curvature quantity and let $R_0$ be the normalized scalar curvature. Yau's second con…