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{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,7,8]],"date-time":"2023-07-08T14:40:44Z","timestamp":1688827244849},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2022,8,3]],"date-time":"2022-08-03T00:00:00Z","timestamp":1659484800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,8,3]],"date-time":"2022-08-03T00:00:00Z","timestamp":1659484800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100009117","name":"Technische Universit\u00e4t Chemnitz","doi-asserted-by":"crossref"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Ann."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>With <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\vec {\\Delta }_j\\ge 0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mml:mrow>\n <mml:msub>\n <mml:mover>\n <mml:mi>\u0394<\/mml:mi>\n <mml:mo>\u2192<\/mml:mo>\n <\/mml:mover>\n <mml:mi>j<\/mml:mi>\n <\/mml:msub>\n <mml:mo>\u2265<\/mml:mo>\n <mml:mn>0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is the uniquely determined self-adjoint realization of the Laplace operator acting on <jats:italic>j<\/jats:italic>-forms on a geodesically complete Riemannian manifold <jats:italic>M<\/jats:italic> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\nabla $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mml:mi>\u2207<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> the Levi-Civita covariant derivative, we prove among other things<jats:list list-type=\"bullet\">\n <jats:list-item>\n <jats:p>a Gaussian heat kernel bound for <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\nabla \\mathrm {e}^{ -t\\vec {\\Delta }_j }$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mml:mrow>\n <mml:mi>\u2207<\/mml:mi>\n <mml:msup>\n <mml:mrow>\n <mml:mi>e<\/mml:mi>\n <\/mml:mrow>\n <mml:mrow>\n <mml:mo>-<\/mml:mo>\n <mml:mi>t<\/mml:mi>\n <mml:msub>\n <mml:mover>\n <mml:mi>\u0394<\/mml:mi>\n <mml:mo>\u2192<\/mml:mo>\n <\/mml:mover>\n <mml:mi>j<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, if the curvature tensor of <jats:italic>M<\/jats:italic> and its covariant derivative are bounded,<\/jats:p>\n <\/jats:list-item>\n <jats:list-item>\n <jats:p>an exponentially weighted <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^p$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mml:msup>\n <mml:mi>L<\/mml:mi>\n <mml:mi>p<\/mml:mi>\n <\/mml:msup>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-bound for the heat kernel of <jats:inline-f
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