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초록· 키워드
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Let $(M,J,\theta)$ be a complete pseudohermintian $(2n+1)$-mani\-fold. In this paper, we derive the subgradient estimate for positive solutions to a nonlinear subelliptic equation $\triangle_b u+a u\log u+b u=0$ on $M$, where $a\leq 0$, $b$ are two real constants.
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참고문헌 (9)
참고문헌 신청
S.-C. Chang / 2011 / Li-Yau grandient estimate and entropy formula for the CR heat equation in a closed pseudohermitian manifold 3-manifold / J. Differential Geometry 89:185~216
S.-C. Chang / CR Li-Yau gradient estimate and linear entropy formula for Witten Laplacian via Bakry-Emery pseudohermitian Ricci curature
S.-C. Chang / Yau's gradient estimate and Liouville theroem for positive pseudoharmonic functions in a complete pseudohermitian manifold
S. Y. Cheng / 1975 / Differential equations on Riemannian manifolds and their geometric applications / Comm. Pure Appl. Math. 28(3):333~354
A. Greenleaf / 1985 / The first eigenvalue of a sublaplacian on a pseudohermitian manifold / Comm. Partial Differential Equations 10(2):191~217
S.-C. Chang / CR Li-Yau gradient estimate and linear entropy formula for Witten Laplacian via Bakry-Emery pseudohermitian Ricci curature
S.-C. Chang / Yau's gradient estimate and Liouville theroem for positive pseudoharmonic functions in a complete pseudohermitian manifold
S. Y. Cheng / 1975 / Differential equations on Riemannian manifolds and their geometric applications / Comm. Pure Appl. Math. 28(3):333~354
A. Greenleaf / 1985 / The first eigenvalue of a sublaplacian on a pseudohermitian manifold / Comm. Partial Differential Equations 10(2):191~217
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