New posts in Riemannian Geometry

What are some examples of incomplete nonextendible manifolds?

Spectral decomposition of $-\Delta$ the Laplacian

Does an injective map stay injective under small smooth perturbations?

How to convince myself (imagine) that $\Bbb S^1$-action on $\Bbb S^3$ fixes a circle of sphere?

Derivative of distance function on a Riemannian manifold.

Existence of curve of constant curvature connecting two points

If $M$ is a compact Riemannian manifold and $g$ and $\tilde{g}$ are metrics on $M$, then $\frac{1}{C} g \leq \tilde{g} \leq C g$ for $C > 1$

Why no flat metric on a sphere?

Quotient of $ S^3 \times S^3$ by a free torus action.

Dirichlet energy in local coordinates