Elliptic and parabolic equations on manifolds, Bochner formulas, minimal surfaces, and the uniformization of surfaces via heat flow.
"That is a minimal surface," Thorne said. "It is the most efficient shape space can take. It is the path light wants to travel. When you look at the moon, you are looking through a tunnel of curved geometry. If the curvature were wrong, if the topology were non-trivial in the wrong way, the light wouldn't reach you. The universe would collapse into a singularity before you could even blink."
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Elliptic and parabolic equations on manifolds, Bochner formulas, minimal surfaces, and the uniformization of surfaces via heat flow.
"That is a minimal surface," Thorne said. "It is the most efficient shape space can take. It is the path light wants to travel. When you look at the moon, you are looking through a tunnel of curved geometry. If the curvature were wrong, if the topology were non-trivial in the wrong way, the light wouldn't reach you. The universe would collapse into a singularity before you could even blink." schoen yau lectures on differential geometry pdf new
Many institutions provide digital PDF access to individual chapters through platforms like Google Books or Semantic Scholar . Purchasing Options Elliptic and parabolic equations on manifolds