The Riemann Surfaces

By Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas. 2011

1,132 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/44aaf7a5f60fdc696bbab3d3be81d1aeab3aabfb

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In Theoretical Computer Science

Citations in the corpus

The Stability Analysis of the Periodic Traveling Wave Solutions of the mKdV Equation (2011, methodology): “This defines a genus one algebraic curve [25], birationally equivalent to (using the normal form algorithm found in [26], and implemented in the Maple command algcurves[Weierstrassform])”
Long‐Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability (2015, background): “In addition, it can be shown that τ ∈ iR+ (see, for example, [32]).”
A solution of an $L^{2}$ extension problem with optimal estimate and applications (2013, background): “g∗F = χ(g)F ), where |χ| = 1 and g is an element of the fundamental group of Ω which naturally acts on the universal covering of Ω (see [23]).”
A solution of an L 2 extension problem with an optimal estimate and applications (2015, background): “g∗F = χ(g)F ), where |χ| = 1 and g is an element of the fundamental group of Ω which naturally acts on the universal covering of Ω (see [19]).”
Calderon inverse Problem with partial data on Riemann Surfaces (2009, methodology): “We start by recalling few elementary definitions and results about Riemann surfaces, see for instance [10] for more details.”
Bordered Riemann surfaces in C2 (2007, background): “For the general theory of Riemann surfaces see [4,17,26,41], and for the theory of Stein manifolds see [27].”
Iteration of Rational Functions (2015, methodology): “Good places to start reading further are (Blanchard 1984), (Milnor 2006), (McMullen 2011) and (Beardon 1991).”
Spectral rigidity and invariant distributions on Anosov surfaces (2012, background): “Since M is non hyperelliptic, the Max Noether theorem [15] together with Lemma 2.”
Period Mappings and Period Domains (2017, methodology): “However, Donaldson’s book (2011) starts as we do, from Riemann surfaces, and focusses on Hodge theory.”
Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A (2015, background): “For textbook presentations of the subject of Riemann surfaces, see Farkas– Kra [186], Fischer [189], Griffiths [221], For textbooks on algebraic curves, see Brieskorn–Knörrer [74], and Ueno [558].”
The Deligne–Mumford compactification of the real multiplication locus and Teichmüller curves in genus 3 (2012, methodology): “Following Wolpert [Wol89] we give explicit holomorphic coordinates at the boundary of Mg and a model of the universal curve in these coordinates.”