Dexterous manipulation with multi-fingered robot hands promises human-level dexterity, but collecting large-scale dexterous robot hand data remains difficult. Learning from human demonstrations has emerged as a scalable alternative to robot teleoperation, providing strong priors on object interaction and contact strategies. Recent sim-to-real RL methods incorporate such priors, but often (i) omit rewards that explicitly incentivize precise contact, yielding weak real-world performance, and/or (ii) generalize poorly to unseen object instances. We propose DemoMimic (Dexterous Motion Mimic), a policy that manipulates objects by focusing on their geometry local to the contact points. Its contact-centric rewards encourage precise contact and improve sim-to-real consistency, yielding a single real-world policy that transfers across objects of varying shape, scale, mass, and friction wherever local contact structure is preserved. Real-world ablations show that DemoMimic achieves 71% success across 16 objects, four tasks, and two robot-hand embodiments, with the smallest sim-to-real drop compared to baselines.

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