Zobrazeno 1 - 10
of 71
pro vyhledávání: '"William P. Minicozzi"'
Publikováno v:
International Mathematics Research Notices. 2022:11878-11890
We prove monotonicity of a parabolic frequency on static and evolving manifolds without any curvature or other assumptions. These are parabolic analogs of Almgren’s frequency function. When the static manifold is Euclidean space and the drift opera
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::83236aa06c0089f6a937ec068580a35e
https://doi.org/10.1093/imrn/rnab052
https://doi.org/10.1093/imrn/rnab052
Publikováno v:
Annales de l'Institut Fourier. 69:2973-3016
Parabolic geometric flows have the property of smoothing for short time however, over long time, singularities are typically unavoidable, can be very nasty and may be impossible to classify. The idea of this paper is that, by bringing in the dynamica
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c05d11e8e4ba32579c4a963e765d2c55
https://doi.org/10.5802/aif.3343
https://doi.org/10.5802/aif.3343
Publikováno v:
Duke Mathematical Journal. 170
For any manifold with polynomial volume growth, we show that the dimension of the space of ancient caloric functions with polynomial growth is bounded by the degree of growth times the dimension of harmonic functions with the same growth. As a conseq
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5da325c1938a31eb8adea871995186f3
https://doi.org/10.1215/00127094-2021-0015
https://doi.org/10.1215/00127094-2021-0015
Publikováno v:
IMRN: International Mathematics Research Notices; Jul2022, Vol. 2022 Issue 15, p11878-11890, 13p
Publikováno v:
Springer Berlin Heidelberg
We first bound the codimension of an ancient mean curvature flow by the entropy. As a consequence, all blowups lie in a Euclidean subspace whose dimension is bounded by the entropy and dimension of the evolving submanifolds. This drastically reduces
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d290992844b1949ce3c620d2d9ee2e24
https://hdl.handle.net/1721.1/131938
https://hdl.handle.net/1721.1/131938
Publikováno v:
Geometric Analysis ISBN: 9783030349523
arXiv
arXiv
© 2020, Springer Nature Switzerland AG. By a classical result, solutions of analytic elliptic PDEs, like the Laplace equation, are analytic. In many instances, the properties that come from being analytic are more important than analyticity itself.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3207cb4f95b5c9dd134b000bd57ff7d1
https://doi.org/10.1007/978-3-030-34953-0_4
https://doi.org/10.1007/978-3-030-34953-0_4
Publikováno v:
arXiv
We showed earlier that the level set function of a monotonic advancing front is twice differentiable everywhere with bounded second derivative and satisfies the equation classically. We show here that the second derivative is continuous if and only i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::21867e38111e2f53513d42e8289d421f
https://doi.org/10.1002/cpa.21703
https://doi.org/10.1002/cpa.21703
Publikováno v:
arXiv
The classical Liouville theorem states that a bounded harmonic function on allofRnmust be constant. In the early 1970s, S.T. Yau vastly generalized this, showing that itholds for manifolds with nonnegative Ricci curvature. Moreover, he conjectured a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c1e9a6fa0326a9a14a62d9704cfb3b1
https://hdl.handle.net/1721.1/124164
https://hdl.handle.net/1721.1/124164
Autor:
William P. Minicozzi
Publikováno v:
Bulletin of the American Mathematical Society. 54:529-532
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5b1fb9123477ad29a8509244b1ac803c
https://doi.org/10.1090/bull/1562
https://doi.org/10.1090/bull/1562