Mohan Ramachandran
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Registered User
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May 13 |
answered | Stein manifolds definiton |
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May 7 |
revised |
Hyperbolic Riemann Surface added 229 characters in body |
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May 6 |
revised |
Hyperbolic Riemann Surface deleted 26 characters in body |
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May 6 |
answered | Hyperbolic Riemann Surface |
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May 6 |
answered | Green’s function - Hyperbolic Riemann surface |
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May 5 |
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Affine varieties as Stein surfaces @kaavek. Varieties can be singular. |
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May 5 |
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Affine varieties as Stein surfaces Affine varieties over complex numbers are always Stein spaces. |
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May 3 |
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Hyperbolic Riemann Surface If you look at the tags it looks like theOP is interested in the existence of positive Green's function which is certainly true for many values of the radius of the disc that is removed. |
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Apr 9 |
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Volume of complex submanifolds This is a consequence of the lower bound for volumes of intersection of analytic sets with ball of fixed radius with center on the analytic set.See for example page 190 of Chirka Complex Analytic Sets |
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Apr 8 |
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A question from Otto Forster’s book on Riemann surfaces The argument is similar to the proof of Nakayama's lemma .Take everything on (1) to one side and multiply by the adjugate matrix. t |
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Apr 5 |
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Injectivity radius of the completion of a manifold If the injectivity radius is strictly positive the metric is automatically complete. |
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Apr 5 |
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noncompact manifold with two ends splits? @Agol: I believe you mean non-negative curvature. |
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Apr 4 |
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Is there non-simple-connected projective variety(over C) with trivial etale fundamental group? For the question exactly as stated in the body of the question the answer is yes since any finitely presented group is the fundamental group of a compact complex manifold. |
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Mar 21 |
awarded | ● Enlightened |
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Mar 21 |
awarded | ● Nice Answer |
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Jan 23 |
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Differential equations and axiom of choice A similar proof can be found in the paper of Wolfgang Walter American Math Monthly vol 78 1971 pages 170-173 . |
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Jan 21 |
answered | classification of non-compact Riemannian manifold with Ric>=-(n-1),and first eigenvalue λ=(n-1)^2/4 |
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Jan 19 |
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Essential uniqueness of the real-analytic structure on $\mathbb R$ Yes.One needs a elliptic PDE with real analytic coefficients.One of the reasons SCV is complicated is that the PDE is overdermined elliptic system . |
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Jan 19 |
accepted | Essential uniqueness of the real-analytic structure on $\mathbb R$ |
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Jan 17 |
answered | When is a smooth projective variety a fibration |
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Jan 17 |
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Essential uniqueness of the real-analytic structure on $\mathbb R$ In fact Bochner showed real analytic embedding of compact real analytic manifolds with real analytic metrics in euclidean by using eigenfunctions of the laplacian. |
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Jan 17 |
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Essential uniqueness of the real-analytic structure on $\mathbb R$ The only other technique I know is to use existence of real analytic metrics and work with harmonic functions for these metrics .However all constructions I know of real analytic metrics are by complex analytic methods . |
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Jan 17 |
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Essential uniqueness of the real-analytic structure on $\mathbb R$ It is a very difficult open problem to prove theorems about real analytic manifolds without complexifying. |
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Jan 17 |
answered | Essential uniqueness of the real-analytic structure on $\mathbb R$ |
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Dec 24 |
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how many nonparabolic ends guarantee a nonconstant harmonic function on Riemannian manifold? Yes there is no control over growth of these functions.OP only asked about nonconstant harmonic functions .In the case of parabolic ends one can find a proper harmonic function along that end.This is a theorem of Mitsuru Nakai. |
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Dec 24 |
answered | how many nonparabolic ends guarantee a nonconstant harmonic function on Riemannian manifold? |
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Dec 23 |
awarded | ● Yearling |
