Quadratic tilt-excess decay and strong maximum principle for varifolds

Reiner Schätzle[1]

  • [1] Mathematisches Institut Rheinischen Friedrich-Wilhelms-Universität Bonn Beringstraße 6, D-53115 Bonn, Germany

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2004)

  • Volume: 3, Issue: 1, page 171-231
  • ISSN: 0391-173X

Abstract

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In this paper, we prove that integral n -varifolds μ in codimension 1 with H μ ∈ L loc p ( μ ) , p > n , p ≥ 2 have quadratic tilt-excess decay tiltex μ ( x , ϱ , T x μ ) = O x ( ϱ 2 ) for μ -almost all x , and a strong maximum principle which states that these varifolds cannot be touched by smooth manifolds whose mean curvature is given by the weak mean curvature H μ , unless the smooth manifold is locally contained in the support of μ .

How to cite

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Schätzle, Reiner. "Quadratic tilt-excess decay and strong maximum principle for varifolds." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.1 (2004): 171-231. <http://eudml.org/doc/84524>.

@article{Schätzle2004,
abstract = {In this paper, we prove that integral $n$-varifolds $\mu $ in codimension 1 with $H_\mu \in L^p_\{\mathrm \{loc\}\nolimits \} (\mu )$, $p &gt; n$, $p \ge 2$ have quadratic tilt-excess decay $\mathrm \{tiltex\}_\mu (x,\varrho ,T_x \mu ) = O_x(\varrho ^2)$for $\mu $-almost all $x$, and a strong maximum principle which states that these varifolds cannot be touched by smooth manifolds whose mean curvature is given by the weak mean curvature $H_\mu $, unless the smooth manifold is locally contained in the support of $\mu $.},
affiliation = {Mathematisches Institut Rheinischen Friedrich-Wilhelms-Universität Bonn Beringstraße 6, D-53115 Bonn, Germany},
author = {Schätzle, Reiner},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {varifolds; strong maximum principle},
language = {eng},
number = {1},
pages = {171-231},
publisher = {Scuola Normale Superiore, Pisa},
title = {Quadratic tilt-excess decay and strong maximum principle for varifolds},
url = {http://eudml.org/doc/84524},
volume = {3},
year = {2004},
}

TY - JOUR
AU - Schätzle, Reiner
TI - Quadratic tilt-excess decay and strong maximum principle for varifolds
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2004
PB - Scuola Normale Superiore, Pisa
VL - 3
IS - 1
SP - 171
EP - 231
AB - In this paper, we prove that integral $n$-varifolds $\mu $ in codimension 1 with $H_\mu \in L^p_{\mathrm {loc}\nolimits } (\mu )$, $p &gt; n$, $p \ge 2$ have quadratic tilt-excess decay $\mathrm {tiltex}_\mu (x,\varrho ,T_x \mu ) = O_x(\varrho ^2)$for $\mu $-almost all $x$, and a strong maximum principle which states that these varifolds cannot be touched by smooth manifolds whose mean curvature is given by the weak mean curvature $H_\mu $, unless the smooth manifold is locally contained in the support of $\mu $.
LA - eng
KW - varifolds; strong maximum principle
UR - http://eudml.org/doc/84524
ER -

References

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