div class=ts-pagebutton class=gotoPage data-page=1Page 1button div class=ts-imageimg data-url=pdst11-sphere-hw-hg94pdst11pdst11-22-the-laplace-operator-on-the-spherehtmlpage=1 data-page=1 class=ts-thumb lazyload alt=Page 1: pdst11 sphere - HWhg94pdst11pdst11_spherepdf · §22 The Laplace Operator on the Sphere 221 The Laplace operator on a Riemannian manifold 1 Let M a manifold with a Riemannian loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader035vdocumentsusreader035viewer20220710055fc2a03fd1ea2e18d465aff4html5thumbnails1jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=2Page 2button div class=ts-imageimg data-url=pdst11-sphere-hw-hg94pdst11pdst11-22-the-laplace-operator-on-the-spherehtmlpage=2 data-page=2 class=ts-thumb lazyload alt=Page 2: pdst11 sphere - HWhg94pdst11pdst11_spherepdf · §22 The Laplace Operator on the Sphere 221 The Laplace operator on a Riemannian manifold 1 Let M a manifold with a Riemannian loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader035vdocumentsusreader035viewer20220710055fc2a03fd1ea2e18d465aff4html5thumbnails2jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=3Page 3button div class=ts-imageimg data-url=pdst11-sphere-hw-hg94pdst11pdst11-22-the-laplace-operator-on-the-spherehtmlpage=3 data-page=3 class=ts-thumb lazyload alt=Page 3: pdst11 sphere - HWhg94pdst11pdst11_spherepdf · §22 The Laplace Operator on the Sphere 221 The Laplace operator on a Riemannian manifold 1 Let M a manifold with a Riemannian loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader035vdocumentsusreader035viewer20220710055fc2a03fd1ea2e18d465aff4html5thumbnails3jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=4Page 4button div class=ts-imageimg data-url=pdst11-sphere-hw-hg94pdst11pdst11-22-the-laplace-operator-on-the-spherehtmlpage=4 data-page=4 class=ts-thumb lazyload alt=Page 4: pdst11 sphere - HWhg94pdst11pdst11_spherepdf · §22 The Laplace Operator on the Sphere 221 The Laplace operator on a Riemannian manifold 1 Let M a manifold with a Riemannian loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader035vdocumentsusreader035viewer20220710055fc2a03fd1ea2e18d465aff4html5thumbnails4jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=5Page 5button div class=ts-imageimg data-url=pdst11-sphere-hw-hg94pdst11pdst11-22-the-laplace-operator-on-the-spherehtmlpage=5 data-page=5 class=ts-thumb lazyload alt=Page 5: pdst11 sphere - HWhg94pdst11pdst11_spherepdf · §22 The Laplace Operator on the Sphere 221 The Laplace operator on a Riemannian manifold 1 Let M a manifold with a Riemannian loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader035vdocumentsusreader035viewer20220710055fc2a03fd1ea2e18d465aff4html5thumbnails5jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=6Page 6button div class=ts-imageimg data-url=pdst11-sphere-hw-hg94pdst11pdst11-22-the-laplace-operator-on-the-spherehtmlpage=6 data-page=6 class=ts-thumb lazyload alt=Page 6: pdst11 sphere - HWhg94pdst11pdst11_spherepdf · §22 The Laplace Operator on the Sphere 221 The Laplace operator on a Riemannian manifold 1 Let M a manifold with a Riemannian loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader035vdocumentsusreader035viewer20220710055fc2a03fd1ea2e18d465aff4html5thumbnails6jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=7Page 7button div class=ts-imageimg data-url=pdst11-sphere-hw-hg94pdst11pdst11-22-the-laplace-operator-on-the-spherehtmlpage=7 data-page=7 class=ts-thumb lazyload alt=Page 7: pdst11 sphere - HWhg94pdst11pdst11_spherepdf · §22 The Laplace Operator on the Sphere 221 The Laplace operator on a Riemannian manifold 1 Let M a manifold with a Riemannian loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader035vdocumentsusreader035viewer20220710055fc2a03fd1ea2e18d465aff4html5thumbnails7jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=8Page 8button div class=ts-imageimg data-url=pdst11-sphere-hw-hg94pdst11pdst11-22-the-laplace-operator-on-the-spherehtmlpage=8 data-page=8 class=ts-thumb lazyload alt=Page 8: pdst11 sphere - HWhg94pdst11pdst11_spherepdf · §22 The Laplace Operator on the Sphere 221 The Laplace operator on a Riemannian manifold 1 Let M a manifold with a Riemannian loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader035vdocumentsusreader035viewer20220710055fc2a03fd1ea2e18d465aff4html5thumbnails8jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=9Page 9button div class=ts-imageimg data-url=pdst11-sphere-hw-hg94pdst11pdst11-22-the-laplace-operator-on-the-spherehtmlpage=9 data-page=9 class=ts-thumb lazyload alt=Page 9: pdst11 sphere - HWhg94pdst11pdst11_spherepdf · §22 The Laplace Operator on the Sphere 221 The Laplace operator on a Riemannian manifold 1 Let M a manifold with a Riemannian loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader035vdocumentsusreader035viewer20220710055fc2a03fd1ea2e18d465aff4html5thumbnails9jpg width=140 height=200 divdivdiv class=ts-pagebutton class=gotoPage data-page=10Page 10button div class=ts-imageimg data-url=pdst11-sphere-hw-hg94pdst11pdst11-22-the-laplace-operator-on-the-spherehtmlpage=10 data-page=10 class=ts-thumb lazyload alt=Page 10: pdst11 sphere - HWhg94pdst11pdst11_spherepdf · §22 The Laplace Operator on the Sphere 221 The Laplace operator on a Riemannian manifold 1 Let M a manifold with a Riemannian loading=lazy src=data:imagegifbase64iVBORw0KGgoAAAANSUhEUgAAAAIAAAACCAQAAADYv8WvAAAAD0lEQVR42mP8X8AwAgiABKBAv+vAXklAAAAAElFTkSuQmCC data-src=https:reader035vdocumentsusreader035viewer20220710055fc2a03fd1ea2e18d465aff4html5thumbnails10jpg width=140 height=200 divdiv