9 problems

Harmonic extension conjecture. The admissible boundary map can be extended to a harmonic map from $X$ to $Y$ with bounded energy density if and only if the inverse image under the…

Non-expansiveness conjecture. The resolvent in should be non-expansive.

The paper considers generalized gradient flows and convex optimization on entanglement polytopes in Hadamard manifolds. In particular, the preceding discussion uses unitary matrice…

Let $M$ be a Riemannian manifold of dimension at least $3$, and let $x_1,x_2,x_3\in M$. Their convex hull is the smallest convex subset of $M$ containing these three points. Berger…

Let $X$ and $Y$ be Hadamard manifolds, let $C<1$, and let $\mathcal{L}_{X,Y}(C)$ denote the optimal Lipschitz constant for extending every $C$-Lipschitz map from a subset of $X$ to…

Let $C<1$. For Hadamard manifolds $X$ and $Y$ satisfying … write $\mathcal{L}_{X,Y}(C)$ for the optimal Lipschitz constant needed to extend every $C$-Lipschitz map from a subset of…

Let $M^{n}$, with $n\geqslant3$, be a simply connected Hadamard manifold whose sectional curvature satisfies … where $k_{1}$ and $k_{2}$ are positive constants. Let…

Let $M$ be a Hadamard manifold and let $\Omega\subset M$ be a mean-convex domain that is not strictly convex at infinity. Write $\partial^{ct}\Omega$ for its ideal and finite bound…

Hadamard manifold isoperimetric inequality conjecture. Every Hadamard manifold satisfies the isoperimetric inequality of $X_\kappa$ whenever $K_N\leqslant\kappa$; equivalently, for…