Journal ArticleDOI
Unique continuation in geometry
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This article is published in Communications on Pure and Applied Mathematics.The article was published on 1988-07-01. It has received 120 citations till now. The article focuses on the topics: Continuation.read more
Citations
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On the Asymptotics for the Vacuum Einstein Constraint Equations
Justin Corvino,Richard Schoen +1 more
TL;DR: In this article, the density of asymptotically flat solutions with harmonic Asymptotics was shown to be a dense subset of the full set of solutions in general classes of solutions of the vacuum constraint equations.
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Bochner's Method for Cell Complexes and Combinatorial Ricci Curvature
TL;DR: A combinatorial analogue of Bochner's theorems is derived, which demonstrates that there are topological restrictions to a space having a cell decomposition with everywhere positive curvature.
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A strong unique continuation theorem for parabolic equations
TL;DR: The unique continuation theorem for second order linear parabolic operators with time-independent coefficients was shown in this article, where the authors relax the smoothness hypotheses on the coefficients and show that even a non-analytic solution of an elliptic equation can behave somewhat in an analytic manner.
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Carleman inequalities and the heat operator
TL;DR: In this article, a strong unique continuation theorem for functions u vanishing to infinite order in the space-time variables at (0, 0) and verifying the inequality |4u+∂tu| ≤ |V (x, t)u| on Rn×(0, T ), when t1− n 2r− 1 s V (x and t) ∈ Lt,locL r x, n/2r+1/s ≤ 1,n/2 < r ≤ ∞.
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Zero sets of solutions to semilinear elliptic systems of first order
TL;DR: In this paper, it was shown that the zero set of the solution is contained in a countable union of smooth (n−2)-dimensional submanifolds and its Hausdorff dimension is at most n−2.
References
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Estimates for the complex and analysis on the heisenberg group
G. B. Folland,E. M. Stein +1 more
Journal Article
Monotonicity properties of variational integrals, ap weights and unique continuation
N Garofalo,Fang-Hua Lin +1 more
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Unique continuation for elliptic operators: A geometric‐variational approach
Nicola Garofalo,Fanghua Lin +1 more
TL;DR: In this article, a sous-ensemble connexe ouvert, Ω de R n, n≥3, on considere l'equation d'ordre 2: Lu=−div(A(x)⊇u)+b(x )•⊈u+V (x)u=0 ou A(x)=(a id j(x)) est une matrice symetrique reelle.
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A unique continuation theorem for exterior differential forms on Riemannian manifolds
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$Q$ valued functions minimizing Dirichlet's integral and the regularity of area minimizing rectifiable currents up to codimension two
TL;DR: In this article, the authors showed that the Hausdorff dimension of the branch set of such a minimizing covering does not exceed m − 2, i.e., when / > 2.