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Nearshore incised valleys are important conduits for the transport of sediment, nutrients, pollutants and organic carbon from the continents to the sea. Therefore, it is essential to understand the autogenic evolution of deltas confined within incised valleys and how such evolution is affected by relative sea‐level rise. To date, limited research has focused on how deltas constrained by incised valleys or other forms of antecedent topography respond to rising sea level. An existing theory of autostratigraphy envisages scenarios in which two‐dimensional or unconfined three‐dimensional fan deltas can experience three evolutionary stages under constant rates of relative sea‐level rise and sediment supply: progradation, autoretreat and post‐autobreak transgression. In this work, an integrated study of geometric numerical models and physical experiments is undertaken to investigate autostratigraphic delta evolution for a variety of incised‐valley geometries, under conditions of constant rates of relative sea‐level rise and sediment supply. Results indicate that interplays of antecedent topography (valley geometries) and sediment mass balance expressed in resultant deltaic geometries can result in autogenic changes in shoreline dynamics and river avulsion frequency on deltas. The following primary findings arise. (i) Compared to valleys with rectangular and trapezoidal cross‐sectional profiles, valleys with triangular cross‐sections tend to contain deltas that experience faster rates of progradation, autoretreat and post‐autobreak transgression under rising sea level, and exhibit a more prominent convex‐seaward shoreline trajectory. (ii) The shoreline trajectory is also related to delta topset geometry, becoming more convex‐seaward under decreasing topset slopes. (iii) River avulsion frequency on deltas with rising sea level varies markedly across valleys with different geometries, even under the same rate of relative sea‐level rise; this is attributed to the difference in temporal evolution of shoreline migration for different valley geometries and the resultant difference in the delta topset aggradation. This study highlights complexities in responses of sedimentary systems under the confinement of different topographic configurations that have hitherto largely been overlooked in sequence‐stratigraphic models. The findings provide insight into future shoreline behaviour and river avulsion hazard on confined deltas, and for decoding the stratigraphic record. [ABSTRACT FROM AUTHOR]